A New Numerical Technique For Solving Fractional Partial Differential\n Equations

2017/04/09 by Omer Acan, Dumitru Bǎleanu, Acan, Omer +1
Mathematics · #34A08 #34K28 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.48550/arxiv.1704.02575

openalex publication_date 2017/04/09 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28

Abstract

We propose conformable Adomian decomposition method (CADM) for fractional\npartial differential equations (FPDEs). This method is a new Adomian\ndecomposition method (ADM) based on conformable derivative operator (CDO) to\nsolve FPDEs. At the same time, conformable reduced differential transform\nmethod (CRDTM) for FPDEs is briely given and a numerical comparison is made\nbetween this method and the newly introduced CADM. In applied science, CADM can\nbe used as an alternative method to obtain approximate and analytical solutions\nfor FPDEs as CRDTM. In this study, linear and non-linear three problems are\nsolved by these two methods. In these methods, the obtained solutions take the\nform of a convergent series with easily computable algorithms. For the\napplications, the obtained results by these methods are compared to each other\nand with the exact solutions. When applied to FPDEs, it is seem that CADM\napproach produces easy, fast and reliable solutions as CRDTM.\n

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