Convergence and stability of an iteration process and solution of a fractional differential equation

Journal of inequalities and applications

Mohd Jubair¹  Faeem Ali¹  Javid Ali¹ 

[1] Department of Mathematics, Aligarh Muslim University, 202002, Aligarh, India;

关键词: Suzuki’s condition (C);    Contractive-like mapping;    Iteration processes;    Fixed point;    Fractional differential equation;    Uniformly convex Banach space;    47H09;    47H10;    54H25;   

DOI  :  10.1186/s13660-021-02677-w

来源: Springer

【 摘 要 】

In this paper, we prove that a three-step iteration process is stable for contractive-like mappings. It is also proved analytically and numerically that the considered process converges faster than some remarkable iterative processes for contractive-like mappings. Furthermore, some convergence results are proved for the mappings satisfying Suzuki’s condition (C) in uniformly convex Banach spaces. A couple of nontrivial numerical examples are presented to support the main results and the visualization is showed by Matlab. Finally, by utilizing our main result the solution of a nonlinear fractional differential equation is approximated.

【 授权许可】

CC BY