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国际多尺度计算工程期刊

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ISSN 打印: 1543-1649

ISSN 在线: 1940-4352

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A NOVEL APPROACH FOR FINDING APPROXIMATE SOLUTIONS OF FRACTIONAL SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS USING THE FRACTIONAL NATURAL DECOMPOSITION METHOD

卷 17, 册 5, 2019, pp. 507-527
DOI: 10.1615/IntJMultCompEng.2019026164
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摘要

In this work, we propose a new approach to find exact solutions to systems of linear fractional partial differential equations (PDEs) using the Fractional Natural Decomposition Method (FNDM). We were be able to find exact solutions for different values of α and β, specifically when α = β = 1, 3/4, 1/2, and 1/4. To the best of our knowledge, we are the first to find such exact solutions for the proposed systems. We employ the FNDM to obtain approximate numerical solutions for two systems of fractional linear PDEs. The FNDM is investigated for these systems of equations and is calculated in the form of power series. The numerical computations in the tables show that our analytical solutions converge very rapidly to the exact solutions.

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对本文的引用
  1. Alrawashdeh Mahmoud S, Bani-Issa Shifaa, An efficient technique to solve coupled–time fractional Boussinesq–Burger equation using fractional decomposition method, Advances in Mechanical Engineering, 13, 6, 2021. Crossref

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