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

[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.

[学科分类] 航空航天科学

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