Unbounded Solutions for a Fractional Boundary Value Problems on the Infinite Interval

Abstract

In this paper, we consider the fractional boundary value problemwhere D a 0+ is the standard Riemann-Liouville fractional derivative. By means of fixed point theorems, sufficient conditions are obtained that guarantee the existence of solutions to the above boundary value problem. The fractional modeling is a generalization of the classical integer-order differential equations and it is a very important tool for modeling the anomalous dynamics of numerous processes involving complex systems found in many diverse fields of science and engineering.

Existence of solutions to initial value problems for nonlinear fractional differential equations on the semi-axis

“…A similar remark is valid for the paper by Zhao and Ge [7], too. Unlike them, in our paper we are working on the whole space C 1−α (R + ).…”

“…We point out that neither Theorem 3.1 in the paper by Kou, Zhou and Yan [3], nor Theorem 4.1 in the paper by Zhao and Ge [7] can be applied to (4.17).…”

“…On the other hand, Zhao and Ge [7] worked in their paper under the assumption that f satisfies an inequality of the form |f (t, x)| ≤ p(t)ω |x| 1 + t α−1 .…”

Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

“…Results on the existence of solutions of boundary value problems on infinite intervals for differential, difference and integral equations may be found in the monographs [19,20]. For boundary value problems of fractional order on infinite intervals we refer to [21]- [25].…”

Solvability for integral boundary value problems of fractional differential equation on infinite intervals

“…Boundary value problems for fractional differential equations on infinite intervals have been considered widely and there are some excellent results on the existence of solutions, see [6,18,25] and the references therein. However, to our knowledge, it is rare for works to be done on the solutions for integral boundary value problems (IBVPs) of fractional differential equations on infinite interval.…”