Cabada, A.; Wanassi, O.K. Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions. Mathematics2020, 8, 255.
Cabada, A.; Wanassi, O.K. Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions. Mathematics 2020, 8, 255.
Cabada, A.; Wanassi, O.K. Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions. Mathematics2020, 8, 255.
Cabada, A.; Wanassi, O.K. Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions. Mathematics 2020, 8, 255.
Abstract
This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.
Keywords
Fractional Equations; Green's Functions; Integral Boundary Conditions; Fixed Point Index; Existence and Non-existence
Subject
Computer Science and Mathematics, Analysis
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
