On stability analysis and existence of positive solutions for a general non-linear fractional differential equations

Advances in Difference Equations

article

Devi, Amita¹  Kumar, Anoop¹  Baleanu, Dumitru²  Khan, Aziz⁵ 

[1] Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab;Department of Mathematics, Faculty of Art and Sciences, Cankaya University;Institute of Space Science;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics and General Sciences, Prince Sultan University

关键词: Hyers–Ulam stability;    p-Laplacian operator;    Caputo fractional derivative;    Guo–Krasnoselskii’s fixed point theorem;    EU of positive solutions;   

DOI  :  10.1186/s13662-020-02729-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Laplacian operator. Also we investigate the Hyers–Ulam (HU) stability of solutions. For the existence result, we establish the integral form of the FDE by using the Green function and then the existence of a solution is obtained by applying Guo–Krasnoselskii’s fixed point theorem. For our purpose, we also check the properties of the Green function. The uniqueness of the result is established by applying the Banach contraction mapping principle. An example is offered to ensure the validity of our results.

【 授权许可】

CC BY