Abstract
In this paper, we study the existence and uniqueness of solutions for fractional boundary value problems involving nonlocal fractional integral boundary conditions, by means of standard fixed point theorems. Some illustrative examples are also presented. MSC:26A33, 34A08, 34B15.
Highlights
Differential equations with fractional order have recently proved to be valuable tools for the description of hereditary properties of various materials and systems
We study the existence and uniqueness of solutions for the following boundary value problem for the fractional differential equation with nonlocal fractional integral boundary conditions
2 Preliminaries we introduce some notations and definitions of fractional calculus [, ] and present preliminary results needed in our proofs later
Summary
Differential equations with fractional order have recently proved to be valuable tools for the description of hereditary properties of various materials and systems. Many researchers have studied the existence theory for nonlinear fractional differential equations with a variety of boundary conditions; for instance, see the papers [ – ], and the references therein. We study the existence and uniqueness of solutions for the following boundary value problem for the fractional differential equation with nonlocal fractional integral boundary conditions We develop some existence and uniqueness results for the boundary value problem
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