Existence and compatibility of positive solutions for boundary value fractional differential equation with modified analytic kernel

[摘要] In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.

[学科分类] 地球科学(综合)

[关键词] fractional differential equation;boundary value problem;positive solution;fractional Green's function;fixed-point theorem