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

Advances in Difference Equations

Amit Kumar¹  Dumitru Baleanu²  Maysaa Al Qurashi³  Sunil Kumar⁴  Syed Abbas⁵ 

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

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

DOI  :  10.1186/s13662-019-2488-3

来源: DOAJ

【 摘 要 】

Abstract 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 L2 $L_{2}$ and L∞ $L_{\infty }$ 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】

Unknown