A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations

Advances in Difference Equations

article

Kumar, Sunil¹  Kumar, Amit²  Abbas, Syed³  Al Qurashi, Maysaa¹  Baleanu, Dumitru⁴ 

[1] Department of Mathematics, National Institute of Technology;Department of Mathematics, Balarampur College Purulia;School of Basic Sciences, Indian Institute of Technology Mandi;Department of Mathematics, Cankya University;Institute of Space Science

关键词: Homotopy analysis transform method;    Fractional Cauchy reaction–diffusion equation;    Mittag-Leffler function;    Optimal value;   

DOI  :  10.1186/s13662-019-2488-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs). Then mainly we address the error norms $L_{2}$ and $L_{\infty }$ for a convergence study of the proposed method. We also find existence, uniqueness and convergence in the analysis for TFCRDEs. The projected method is illustrated by solving some numerical examples. The obtained numerical solutions by the HATM method show that it is simple to employ. An excellent conformity obtained between the solution got by the HATM method and the various well-known results available in the current literature. Also the existence and uniqueness of the solution have been demonstrated.

【 授权许可】

CC BY