On Fractional Hybrid Non-Linear Differential Equations Involving Three Mixed Fractional Orders with Boundary Conditions

Symmetry

Huiwen Wang¹  Liping Zhang¹  Fang Li¹ 

[1] School of Mathematics, Yunnan Normal University, Kunming 650092, China;

关键词: mixed fractional derivatives;    fractional differential equations;    hybrid differential equations;    boundary value problem;   

DOI  :  10.3390/sym14061189

来源: DOAJ

【 摘 要 】

In this paper, we study a class of non-linear fractional hybrid differential equations involving three mixed fractional orders with boundary conditions. Under weak assumptions, a formula of solutions is constructed and the existence results of the solutions for the problem are established. The results can be used to solve more general fractional hybrid equations, such as the general variable coefficient fractional hybrid Langevin equations. Moreover, the form of the solution for this kind of equation can provide a theoretical basis for the further study of the positive solution and its symmetry. We provide an example to support our main result.

【 授权许可】

Unknown