An Efficient Computational Method for Differential Equations of Fractional Type


TÜRKYILMAZOĞLU M.

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, vol.133, no.1, pp.47-65, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 133 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.32604/cmes.2022.020781
  • Journal Name: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.47-65
  • Keywords: Fractional differential equations, Adomian decomposition method, optimal data, residual error, ADOMIAN DECOMPOSITION METHOD, NUMERICAL-SOLUTIONS, TIME
  • Hacettepe University Affiliated: Yes

Abstract

An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L2 norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical models. Better performance of the method is further evidenced against some compared commonly used numerical techniques.