Abstract
In this paper, we discuss a boundary value problem for an impulsive fractional differential equation. By transforming the boundary value problem into an equivalent integral equation, and employing the Banach fixed point theorem and the Schauder fixed point theorem, existence results for the solutions are obtained. For application, we provide some examples to illustrate our main results.
Highlights
1 Introduction Fractional differential equations have attracted great attention from many researchers because fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various processes in science and engineering, such as physics, control theory, electrochemistry, biology, viscoelasticity, signal processing, nuclear dynamics, etc
See [ – ] and the references therein. Another important class of differential equations is known as impulsive differential equations
Boundary value problems for impulsive fractional differential equations have been attractive to many researchers; see [ – ]
Summary
Fractional differential equations have attracted great attention from many researchers because fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various processes in science and engineering, such as physics, control theory, electrochemistry, biology, viscoelasticity, signal processing, nuclear dynamics, etc. Boundary value problems for impulsive fractional differential equations have been attractive to many researchers; see [ – ]. Tian et al [ ] developed a sufficient condition for the existence of solutions to the impulsive boundary value problem involving the Caputo fractional derivative as follows:
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