Publicou 12 edições por ano
ISSN Imprimir: 1091-028X
ISSN On-line: 1934-0508
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APPLICATION OF REPRODUCING KERNEL ALGORITHM FOR SOLVING DIRICHLET TIME-FRACTIONAL DIFFUSION-GORDON TYPES EQUATIONS IN POROUS MEDIA
RESUMO
Time-fractional partial differential equations describe different phenomena in statistical physics, applied mathematics, and engineering. In this article, we propose and analyze an efficient reproducing kernel algorithm for the numerical solutions of such equations in porous media with Dirichlet boundary conditions. The representation of the exact and the numerical solutions is given in the W (Ω) and H (Ω) inner product spaces, whereas the computation of the required grid points relies on the R(y;s) (x; t) and r(y;s) (x; t) reproducing kernel functions. To confirm the accuracy of the new approach, several numerical examples are implemented, including linear and nonlinear terms that are acquired by interrupting the n-term of the exact solutions. The convergence of the utilized algorithm is studied theoretically and numerically by comparing the exact solutions of the problems under investigation. Finally, the obtained results show the significant improvement of the algorithm while saving the convergence accuracy and time.
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Abu Arqub, O., The Reproducing Kernel Algorithm for Handling Differential Algebraic Systems of Ordinary Differential Equations, Math. Methods Appl. Sci., vol. 39, pp. 4549–4562, 2016a.
-
Abu Arqub, O., Approximate Solutions of DASs with Nonclassical Boundary Conditions using Novel Reproducing Kernel Algorithm, Fundamenta Informaticae, vol. 146, pp. 231–254, 2016b.
-
Abu Arqub, O., Fitted Reproducing Kernel Hilbert Space Method for the Solutions of Some Certain Classes of Time-Fractional Partial Differential Equations Subject to Initial and Neumann Boundary Conditions, Comput. Math. Appl., vol. 73, pp. 1243– 1261, 2017a.
-
Abu Arqub, O., Adaptation of Reproducing Kernel Algorithm for Solving Fuzzy Fredholm-Volterra Integrodifferential Equations, Neural Comput. Appl., vol. 28, pp. 1591–1610, 2017b.
-
Abu Arqub, O., Numerical Solutions for the Robin Time-Fractional Partial Differential Equations of Heat and Fluid Flows based on the Reproducing Kernel Algorithm, Int. J. Numer. Methods Heat Fluid Flow, vol. 28, pp. 828–856, 2018.
-
Abu Arqub, O. and Al-Smadi, M., Numerical Algorithm for Solving Two-Point, Second-Order Periodic Boundary Value Problems for Mixed Integro-Differential Equations, Appl. Math. Comput., vol. 243, pp. 911–922, 2014.
-
Abu Arqub, O., Al-Smadi, M., Momani, S., and Hayat, T., Numerical Solutions of Fuzzy Differential Equations using Reproducing Kernel Hilbert Space Method, Soft Comput., vol. 20, pp. 3283–3302, 2016.
-
Abu Arqub, O., Al-Smadi, M., Momani, S., and Hayat, T., Application of Reproducing Kernel Algorithm for Solving Second- Order, Two-Point Fuzzy Boundary Value Problems, Soft Comput., vol. 21, pp. 7191–7206, 2017.
-
Abu Arqub, O., Al-Smadi, M., and Shawagfeh, N., Solving Fredholm Integro-Differential Equations using Reproducing Kernel Hilbert Space Method, Appl. Math. Comput., vol. 219, pp. 8938–8948, 2013.
-
Abu Arqub, O., El-Ajou, A., and Momani, S., Constructing and Predicting Solitary Pattern Solutions for Nonlinear Time-Fractional Dispersive Partial Differential Equations, J. Comput. Phys., vol. 293, pp. 385–399, 2015.
-
Abu Arqub, O. and Maayah, B., Solutions of Bagley-Torvik and Painlev´e Equations of Fractional Order using Iterative Reproducing Kernel Algorithm, Neural Comput. Appl., vol. 29, pp. 1465–1479, 2018a.
-
Abu Arqub, O. and Maayah, B., Numerical Solutions of Integrodifferential Equations of Fredholm Operator Type in the Sense of the Atangana–Baleanu Fractional Operator, Chaos, Solitons Fractals, vol. 117, pp. 117–124, 2018b.
-
Abu Arqub, O. and Rashaideh, H., The RKHS Method for Numerical Treatment for Integrodifferential Algebraic Systems of Temporal Two-Point BVPs, Neural Comput. Appl., vol. 30, pp. 2595–2606, 2018.
-
Al-Smadi, M., Abu Arqub, O., Shawagfeh, N., and Momani, S., Numerical Investigations for Systems of Second-Order Periodic Boundary Value Problems using Reproducing Kernel Method, Appl. Math. Comput., vol. 291, pp. 137–148, 2016.
-
Aronszajn, N., Theory of Reproducing Kernels, Transact. Am. Math. Soc., vol. 68, pp. 337–404, 1950.
-
Berlinet, A. and Agnan, C.T., Reproducing Kernel Hilbert Space in Probability and Statistics, Boston: Kluwer Academic Publishers, 2004.
-
Chen, A. and Li, C., Numerical Solution of Fractional Diffusion-Wave Equation, Numer. Funct. Anal. Optim., vol. 37, pp. 19–39, 2016.
-
Chen, J., Liu, F., and Anh, V., Analytical Solution for the Time-Fractional Telegraph Equation by the Method of Separating Variables, J. Math. Anal. Appl., vol. 338, pp. 1364–1377, 2008.
-
Comptedag, A. and Metzlerddag, R., The Generalized Cattaneo Equation for the Description of Anomalous Transport Processes, J. Physics A: Math. General, vol. 30, pp. 7277–7289, 1997.
-
Cui, M. and Lin, Y., Nonlinear Numerical Analysis in the Reproducing Kernel Space, New York: Nova Science, 2009.
-
Daniel, A., Reproducing Kernel Spaces and Applications, Basel, Switzerland: Springer, 2003.
-
Das, S., Functional Fractional Calculus for System Identification and Controls, Berlin: Springer, 2008.
-
Dehghan, M. and Safarpoor, M., The Dual Reciprocity Boundary Integral Equation Technique to Solve a Class of the Linear and Nonlinear Fractional Partial Differential Equations, Math. Methods Appl. Sci., vol. 39, pp. 2461–2476, 2016.
-
Diethelm, K., The Analysis of Fractional Differential Equations, Berlin: Springer, 2010.
-
El-Ajou, A., Abu Arqub, O., and Momani, S., Approximate Analytical Solution of the Nonlinear Fractional KdV-Burgers Equation: A New Iterative Algorithm, J. Comput. Phys., vol. 293, pp. 81–95, 2015a.
-
El-Ajou, A., Abu Arqub, O., Momani, S., Baleanu, D., and Alsaedi, A., A Novel Expansion Iterative Method for Solving Linear Partial Differential Equations of Fractional Order, Appl. Math. Comput., vol. 257, pp. 119–133, 2015b.
-
Geng, F.Z. and Cui, M., A Reproducing Kernel Method for Solving Nonlocal Fractional Boundary Value Problems, Appl. Math. Lett., vol. 25, pp. 818–823, 2012.
-
Geng, F.Z. and Qian, S.P., Reproducing Kernel Method for Singularly Perturbed Turning Point Problems Having Twin Boundary Layers, Appl. Math. Lett., vol. 26, pp. 998–1004, 2013.
-
Geng, F.Z. and Qian, S.P., Modified Reproducing Kernel Method for Singularly Perturbed Boundary Value Problems with a Delay, Appl. Math. Modell., vol. 39, pp. 5592–5597, 2015.
-
Geng, F.Z., Qian, S.P., and Li, S., A Numerical Method for Singularly Perturbed Turning Point Problems with an Interior Layer, J. Comput. Appl. Math., vol. 255, pp. 97–105, 2014.
-
Golmankhaneh, A.K., Golmankhaneh, A.K., and Baleanu, D., On Nonlinear Fractional Klein–Gordon Equation, Signal Process., vol. 91, pp. 446–451, 2011.
-
Hilfer, R., Applications of Fractional Calculus in Physics, Singapore: World Scientific, 2000.
-
Jiang, W. and Chen, Z., Solving a System of Linear Volterra Integral Equations using the New Reproducing Kernel Method, Appl. Math. Computat., vol. 219, pp. 10225–10230, 2013.
-
Jiang, W. and Chen, Z., A Collocation Method based on Reproducing Kernel for a Modified Anomalous Subdiffusion Equation, Numer. Methods Partial Diff. Eqs., vol. 30, pp. 289–300, 2014.
-
Jiang,W. and Lin, Y., Approximate Solution of the Fractional Advection-Dispersion Equation, Comput. Phys. Commun., vol. 181, pp. 557–561, 2010.
-
Jiang, W. and Lin, Y., Representation of Exact Solution for the Time Fractional Telegraph Equation in the Reproducing Kernel Space, Commun. Nonlinear Sci. Numer. Simul., vol. 16, pp. 3639–3645, 2011.
-
Kumar, S., Kumar, D., and Singh, J., Numerical Computation of Fractional Black-Scholes Equation Arising in Financial Market, Egypt. J. Basic Appl. Sci., vol. 1, pp. 177–183, 2014.
-
Kumar, S. and Rashidi, M.M., New Analytical Method for Gas Dynamics Equation Arising in Shock Fronts, Comput. Phys. Commun., vol. 185, pp. 1947–1954, 2014.
-
Kumar, D., Singh, J., and Baleanu, D., Numerical Computation of a Fractional Model of Differential-Difference Equation, J. Comput. Nonlinear Dynam., vol. 11, p. 061004, 2016.
-
Kumar, D., Singh, J., Kumar, S., Sushila, and Singh, B.P., Numerical Computation of Nonlinear ShockWave Equation of Fractional Order, Ain Shams Eng. J., vol. 6, pp. 605–611, 2015.
-
Kilbas, A.A.A., Srivastava, H.M., and Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Amsterdam: Elsevier, 2006.
-
Lin, Y., Cui, M., and Yang, L., Representation of the Exact Solution for a Kind of Nonlinear Partial Differential Equations, Appl. Math. Lett., vol. 19, pp. 808–813, 2006.
-
Li, C. and Deng, W., Chaos Synchronization of Fractional-Order Differential Systems, Int. J. Modern Phys. B, vol. 20, pp. 791– 803, 2006.
-
Li, X. and Wu, B., Approximate Analytical Solutions of Nonlocal Fractional Boundary Value Problems, Appl. Math. Modell., vol. 39, pp. 1717–1724, 2015.
-
Magin, R.L., Fractional Calculus Models of Complex Dynamics in Biological Tissues, Comput. Math. Appl., vol. 59, pp. 1586– 1593, 2010.
-
Metzler, R. and Klafter, J., The Random Walk’s Guide to Anomalous Diffusion: A Fractional Dynamics Approach, Phys. Rep., vol. 339, pp. 1–77, 2000.
-
Mohebbi, A. and Dehghan, M., High-Order Solution of One-Dimensional Sine-Gordon Equation using Compact Finite Difference and DIRKN Methods, Math. Comput. Modell., vol. 51, pp. 537–549, 2010.
-
Momani, S., Abu Arqub, O., Hayat, T., and Al-Sulami, H., A Computational Method for Solving Periodic Boundary Value Problems for Integro-Differential Equations of Fredholm–Volterra Type, Appl. Math. Comput., vol. 240, pp. 229–239, 2014.
-
Odibat, Z. and Momani, S., The Variational Iteration Method: An Efficient Scheme for Handling Fractional Partial Differential Equations in Fluid Mechanics, Comput. Math. Appl., vol. 58, pp. 2199–2208, 2009.
-
Ortigueira, M.D. and Machado, J.A.T., Fractional Signal Processing and Applications, Signal Process., vol. 83, pp. 2285–2286, 2003.
-
Rehman, M.U. and Khan, R.A., Numerical Solutions to Initial and Boundary Value Problems for Linear Fractional Partial Differential Equations, Appl. Math. Modell., vol. 37, pp. 5233–5244, 2013.
-
Singh, J., Kumar, D., and Nieto, J.J., A Reliable Algorithm for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow, Entropy, vol. 18, no. 6, p. 206, 2016a. DOI: 10.3390/e18060206
-
Singh, J., Kumar, D., and Swroop, R., Numerical Solution of Time- and Space-Fractional Coupled Burgers Equations via Homotopy Algorithm, Alexandria Eng. J., vol. 55, pp. 1753–1763, 2016b.
-
Singh, J., Rashidi, M.M., Kumar, D., and Swroop, R., A Fractional Model of a Dynamical Brusselator Reaction-Diffusion System Arising in Triple Collision and Enzymatic Reactions, Nonlinear Engineer. Model. Appl., vol. 5, pp. 277–285, 2016c.
-
Srivastava, H.M., Kumar, D., and Singh, J., An Efficient Analytical Technique for Fractional Model of Vibration Equation, Appl. Math. Modell., vol. 45, pp. 192–204, 2017.
-
Sun, Z.Z. and Wu, X., A Fully Discrete Difference Scheme for a Diffusion-Wave System, Appl. Numer. Math., vol. 56, pp. 193– 209, 2006.
-
Tarasova, V.E. and Zaslavsky, G.M., Fractional Dynamics of Systems with Long-Range Space Interaction and Tempolar Memory, Physica A: Statist. Mech. Appl., vol. 383, pp. 291–308, 2007.
-
Vong, S. and Wang, Z., A High-Order Compact Scheme for the Nonlinear Fractional Klein–Gordon Equation, Numer. Methods Part. Diff. Eqs., vol. 31, pp. 706–722, 2015.
-
Weinert, H.L., Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing, London: Hutchinson, 1982.
-
Wang, Q.F. and Cheng, D., Numerical Solution of Damped Nonlinear Klein-Gordon Equations using Variational Method and Finite Element Approach, Appl. Math. Comput., vol. 162, pp. 381–401, 2005.
-
Wang, Y., Du, M., Tan, F., Li, Z., and Nie, T., Using Reproducing Kernel for Solving a Class of Fractional Partial Differential Equation with Non-Classical Conditions, Appl. Math. Comput., vol. 219, pp. 5918–5925, 2013a.
-
Wang, W., Han, B., and Yamamoto, M., Inverse Heat Problem of Determining Time-Dependent Source Parameter in Reproducing Kernel Space, Nonlinear Anal.: Real World Appl., vol. 14, pp. 875–887, 2013b.
-
Yang, L.H. and Lin, Y., Reproducing Kernel Methods for Solving Linear Initial-Boundary-Value Problems, Electron. J. Diff. Eqs., vol. 2008, pp. 1–11, 2008.
-
Yang, L.H., Shen, J.H., and Wang, Y., The Reproducing Kernel Method for Solving the System of the Linear Volterra Integral Equations with Variable Coefficients, J. Comput. Appl. Math., vol. 236, pp. 2398–2405, 2012.
-
Yusufoglu, E., The Variational Iteration Method for Studying the Klein-Gordon Equation, Appl. Math. Lett., vol. 4, pp. 669–674, 2008.
-
Zhoua, Y., Cui, M., and Lin, Y., Numerical Algorithm for Parabolic Problems with Non-Classical Conditions, J. Comput. Appl. Math., vol. 230, pp. 770–780, 2009.
-
Qureshi Sania, Aziz Shaheen, Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel, Physica A: Statistical Mechanics and its Applications, 542, 2020. Crossref
-
Arqub Omar Abu, Maayah Banan, Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations, Chaos, Solitons & Fractals, 126, 2019. Crossref
-
Qureshi Sania, Memon Zaib-un-Nisa, Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan, Chaos, Solitons & Fractals, 131, 2020. Crossref
-
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-
Abu Arqub Omar, Al-Smadi Mohammed, An adaptive numerical approach for the solutions of fractional advection–diffusion and dispersion equations in singular case under Riesz’s derivative operator, Physica A: Statistical Mechanics and its Applications, 540, 2020. Crossref
-
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-
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-
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-
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-
Li X.Y., Wu B.Y., A new kernel functions based approach for solving 1-D interface problems, Applied Mathematics and Computation, 380, 2020. Crossref
-
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-
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-
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-
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-
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-
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-
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-
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-
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-
Yilmaz A., Unal G., Multiscale Higuchi’s fractal dimension method, Nonlinear Dynamics, 101, 2, 2020. Crossref
-
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-
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-
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-
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-
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-
Carrer J.A.M., Solheid B.S., Trevelyan J., Seaid M., A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem, Engineering Analysis with Boundary Elements, 122, 2021. Crossref
-
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-
Youssef Hamdy M., El-Bary Alaa A., The thermal behavior analysis of the human eye under the heat conduction law with one relaxation time, Alexandria Engineering Journal, 59, 6, 2020. Crossref
-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
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-
Mousa Mohamed H., Hussein Mohamed K., Toward high-performance computation of surface approximation using a GPU, Computers and Electrical Engineering, 99, 2022. Crossref
-
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-
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-
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-
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-
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Han Aydın S., Stabilized solution of the 3-D MHD flow problem with FEM–BEM coupling approach, Engineering Analysis with Boundary Elements, 140, 2022. Crossref
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Nisar Kottakkaran Sooppy, Logeswari Kumararaju, Vijayaraj Veliappan, Baskonus Haci Mehmet, Ravichandran Chokkalingam, Fractional Order Modeling the Gemini Virus in Capsicum annuum with Optimal Control, Fractal and Fractional, 6, 2, 2022. Crossref
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Akram Ghazala, Abbas Muhammad, Tariq Hira, Sadaf Maasoomah, Abdeljawad Thabet, Alqudah Manar A., Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique, Fractal and Fractional, 6, 3, 2022. Crossref
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Rehman Sajid, Gul Taza, Khan Waris, Khan Aamir, Zeeshan , Effects of chemical reaction, viscosity, thermal conductivity, heat source, radiation/absorption, on MHD mixed convection nano-fluids flow over an unsteady stretching sheet by HAM and numerical method, Advances in Mechanical Engineering, 14, 1, 2022. Crossref
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Zhao Rundong, Liu Qiming, Sun Meici, Dynamical behavior of a stochastic SIQS epidemic model on scale-free networks, Journal of Applied Mathematics and Computing, 68, 2, 2022. Crossref
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Arqub Omar Abu, Hayat Tasawar, Alhodaly Mohammed, Analysis of Lie Symmetry, Explicit Series Solutions, and Conservation Laws for the Nonlinear Time-Fractional Phi-Four Equation in Two-Dimensional Space, International Journal of Applied and Computational Mathematics, 8, 3, 2022. Crossref
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Wang Fengjie, Sahana Mehebub, Pahlevanzadeh Bahareh, Chandra Pal Subodh, Kumar Shit Pravat, Piran Md. Jalil, Janizadeh Saeid, Band Shahab S., Mosavi Amir, Applying different resampling strategies in machine learning models to predict head-cut gully erosion susceptibility, Alexandria Engineering Journal, 60, 6, 2021. Crossref
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Arafa Anas, Hanafy Ibrahim, Hagag Ahmed, A Laplace substitution method of space‐time fractional order including jumbled partial derivatives, Mathematical Methods in the Applied Sciences, 45, 4, 2022. Crossref
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Beghami Wahiba, Maayah Banan, Bushnaq Samia, Abu Arqub Omar, The Laplace Optimized Decomposition Method for Solving Systems of Partial Differential Equations of Fractional Order, International Journal of Applied and Computational Mathematics, 8, 2, 2022. Crossref
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Alsadi K. S., Bound state solutions of a Dirac particle undergoing a tensor interaction potentials via asymptotic iteration method, Journal of Taibah University for Science, 14, 1, 2020. Crossref
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Ul Abadin Zafar Zain, Rezazadeh Hadi, Inc Mustafa, Nisar Kottakkaran Sooppy, Sulaiman Tukur A., Yusuf Abdullahi, Fractional order heroin epidemic dynamics, Alexandria Engineering Journal, 60, 6, 2021. Crossref
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Kumari M., Barak M.S., Singh A., Kumar M., Effect of various physical properties on the reflection coefficients of inhomogeneous waves at the stress-free surface of partially saturated soils induced by obliquely incident fast P-wave, Journal of Ocean Engineering and Science, 7, 3, 2022. Crossref
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Rabah Ahlem Ben, Momani Shaher, Arqub Omar Abu, The B-spline collocation method for solving conformable initial value problems of non-singular and singular types, Alexandria Engineering Journal, 61, 2, 2022. Crossref
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Liu Chein-Shan, El-Zahar Essam R., Chen Yung-Wei, Solving nonlinear elliptic equations in arbitrary plane domains by using a new splitting and linearization technique, Engineering Analysis with Boundary Elements, 125, 2021. Crossref
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Li Xiuying, Wang Hongliang, Wu Boying, An accurate numerical technique for fractional oscillation equations with oscillatory solutions, Mathematical Methods in the Applied Sciences, 45, 2, 2022. Crossref
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Jaradat Imad, Alquran Marwan, A variety of physical structures to the generalized equal-width equation derived from Wazwaz-Benjamin-Bona-Mahony model, Journal of Ocean Engineering and Science, 7, 3, 2022. Crossref
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Abu Arqub Omar, Singh Jagdev, Alhodaly Mohammed, Adaptation of kernel functions‐based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations, Mathematical Methods in the Applied Sciences, 2021. Crossref
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Phoosree Sirasrete, Thadee Weerachai, Wave Effects of the Fractional Shallow Water Equation and the Fractional Optical Fiber Equation, Frontiers in Applied Mathematics and Statistics, 8, 2022. Crossref
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Misra O. P., Sisodiya Omprakash Singh, Spread and control of COVID-19: A mathematical model, International Journal of Modeling, Simulation, and Scientific Computing, 13, 03, 2022. Crossref
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Arqub Omar Abu, Al-Smadi Mohammed, Almusawa Hassan, Baleanu Dumitru, Hayat Tasawar, Alhodaly Mohammed, Osman M.S., A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves, Alexandria Engineering Journal, 61, 7, 2022. Crossref
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Sánchez Edgar Andrés, Flores Alain, Hernández-Cobos Jorge, Moreno Matías, Antillón Armando, Onset of resonances by roots overlapping using quasi-invariants in nonlinear accelerator dynamics, Nonlinear Dynamics, 2022. Crossref
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Abdel-Khalek S., Khalil E.M., Mohamed A.-B.A., Abdel-Aty M., Besbes H.R., Response of quantum Fisher information, variance entropy squeezing and entanglement to the intrinsic decoherence of two non-degenerate fields interacting with two qubits, Alexandria Engineering Journal, 59, 6, 2020. Crossref
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Chen Liping, Chen Gang, Li Penghua, Lopes António M., Tenreiro Machado J.A., Xu Shuiqing, A variable-order fractional proportional-integral controller and its application to a permanent magnet synchronous motor, Alexandria Engineering Journal, 59, 5, 2020. Crossref
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Patel Hardik , Patel Trushit, ANALYTICAL STUDY OF INSTABILITY PHENOMENON WITH AND WITHOUT INCLINATION IN HOMOGENEOUS AND HETEROGENEOUS POROUS MEDIA USING FRACTIONAL APPROACH , Journal of Porous Media, 25, 9, 2022. Crossref
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Pinheiro Vitor Pancieri, Loeffler Carlos Friedrich, Mansur Webe João, Boundary element method solution of stationary advective–diffusive problems: A comparison between the direct interpolation and dual reciprocity technique, Engineering Analysis with Boundary Elements, 142, 2022. Crossref
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Al-Deiakeh Rawya, Abu Arqub Omar, Al-Smadi Mohammed, Momani Shaher, Lie symmetry analysis, explicit solutions, and conservation laws of the time-fractional Fisher equation in two-dimensional space, Journal of Ocean Engineering and Science, 7, 4, 2022. Crossref
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Khan Dolat, Ali Gohar, Kumam Poom, Rahman Ata ur, Watthayu Wiboonsak, Galal Ahmed M., Free convective couette flow analysis of viscoelastic dusty fluid along with Newtonian heating in a rotating frame, Waves in Random and Complex Media, 2022. Crossref
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Mandal Gopinath, Pal Dulal, ENTROPY GENERATION ANALYSIS OF MAGNETOHYDRODYNAMIC DARCY-FORCHHEIMER WILLIAMSON HYBRID NANOFLUID FLOW THROUGH POROUS MEDIUM WITH NONLINEAR THERMAL RADIATION , Special Topics & Reviews in Porous Media: An International Journal, 13, 3, 2022. Crossref
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Jiang Jingang, Tan Qiyun, Yu Xiaoyang, Wu Dianhao, Yao Liang, Research Progress of Bionic Water Strider Robot, Recent Patents on Mechanical Engineering, 15, 2, 2022. Crossref
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Sweis Hind, Shawagfeh Nabil, Abu Arqub Omar, Fractional crossover delay differential equations of Mittag-Leffler kernel: Existence, uniqueness, and numerical solutions using the Galerkin algorithm based on shifted Legendre polynomials, Results in Physics, 41, 2022. Crossref
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Ullah Ikram, Ullah Zakir , Zaman Gul, Alam M.M. , EFFECT OF HEAT SOURCE ON STAGNATION-POINT MHD TANGENT HYPERBOLIC FLUID FLOW ON A STRETCHED SHEET IN A POROUS MEDIUM , Special Topics & Reviews in Porous Media: An International Journal, 13, 3, 2022. Crossref
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Djilali Salih, Bentout Soufiane, Kumar Sunil, Touaoula Tarik Mohammed, Approximating the asymptomatic infectious cases of the COVID-19 disease in Algeria and India using a mathematical model, International Journal of Modeling, Simulation, and Scientific Computing, 13, 04, 2022. Crossref
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Abu Arqub Omar, Tayebi Soumia, Baleanu Dumitru, Osman M.S., Mahmoud W., Alsulami Hamed, A numerical combined algorithm in cubic B-spline method and finite difference technique for the time-fractional nonlinear diffusion wave equation with reaction and damping terms, Results in Physics, 41, 2022. Crossref
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Prasad Madasu Krishna , Sarkar Priya , A STUDY OF COUPLE STRESS FLUID PAST AN ISOTROPIC POROUS MEDIUM , Special Topics & Reviews in Porous Media: An International Journal, 13, 4, 2022. Crossref
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Kumar Manjeet , Kaswan Pradeep, Kumari Manjeet, NUMERICAL SIMULATION OF ENTROPY GENERATION ANALYSIS OF MHD HYBRID-NANOFLUID FLOW WITH NONLINEAR THERMAL RADIATION AND MELTING HEAT TRANSFER , Special Topics & Reviews in Porous Media: An International Journal, 13, 6, 2022. Crossref
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Partohaghighi Mohammad, Akgül Ali, Akgül Esra Karatas, Attia Nourhane, De la Sen Manuel, Bayram Mustafa, Analysis of the Fractional Differential Equations Using Two Different Methods, Symmetry, 15, 1, 2022. Crossref
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Maji Chandan, Impact of media coverage on a fractional-order SIR epidemic model, International Journal of Modeling, Simulation, and Scientific Computing, 13, 05, 2022. Crossref