Abstract
In this paper, we study the existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Riemann-Liouville type fractional derivatives with the nonlocal Katugampola fractional integral conditions. A variety of fixed point theorems are used such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder degree theory. Enlightening examples of the obtained results are also presented.
Highlights
We investigate the sufficient conditions of the existence of solutions for the following fractional Langevin equation subject to the generalized nonlocal fractional integral conditions of the form:
More and more researchers have found that fractional differential equations play important roles in many research areas, such as physics, chemical technology, population dynamics, biotechnology, and economics
In this paper we study the boundary value problem ( . ) with generalized fractional integral boundary conditions
Summary
We investigate the sufficient conditions of the existence of solutions for the following fractional Langevin equation subject to the generalized nonlocal fractional integral conditions of the form: [ ] The Riemann-Liouville fractional integral of order p > of a continuous function f : ( , ∞) → R is defined by [ ] The Riemann-Liouville fractional derivative of order p > of a continuous function f : ( , ∞) → R is defined by
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