Non-Trivial Solutions of Non-Autonomous Nabla Fractional Difference Boundary Value Problems

Symmetry

Alberto Cabada¹  Jagan Mohan Jonnalagadda²  Nikolay D. Dimitrov³ 

[1] Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain;Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500078, India;Department of Mathematics, University of Ruse, 7017 Ruse, Bulgaria;

关键词: nabla fractional difference;    boundary value problem;    separated boundary conditions;    Green’s function;    existence of solutions;   

DOI  :  10.3390/sym13061101

来源: DOAJ

【 摘 要 】

In this article, we present a two-point boundary value problem with separated boundary conditions for a finite nabla fractional difference equation. First, we construct an associated Green’s function as a series of functions with the help of spectral theory, and obtain some of its properties. Under suitable conditions on the nonlinear part of the nabla fractional difference equation, we deduce two existence results of the considered nonlinear problem by means of two Leray–Schauder fixed point theorems. We provide a couple of examples to illustrate the applicability of the established results.

【 授权许可】

Unknown