Abstract
In this paper, by using some fixed point theorems and the measure of noncompactness, we discuss the existence of solutions for a boundary value problem of impulsive integrodifferential equations of fractional order alphain(1,2]. Our results improve and generalize some known results in (Zhou and Chu in Commun. Nonlinear Sci. Numer. Simul. 17:1142-1148, 2012; Bai et al. in Bound. Value Probl. 2016:63, 2016). Finally, an example is given to illustrate that our result is valuable.
Highlights
1 Introduction Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, and they have been emerging as an important area of investigation in the last few decades; see [ – ]
The theory of impulsive differential equations is a new and important branch of differential equation theory, which has an extensive physical, population dynamics, ecology, chemical, biological systems, and engineering background. It has been an object of intensive investigation in recent years, some basic results on impulsive differential equations have been obtained and applications to different areas have been considered by many authors, see [ – ]
In this paper, motivated by the above references, we investigate the existence of solutions to the following impulsive fractional integro-differential equations with mixed boundary conditions:
Summary
Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, and they have been emerging as an important area of investigation in the last few decades; see [ – ].The theory of impulsive differential equations is a new and important branch of differential equation theory, which has an extensive physical, population dynamics, ecology, chemical, biological systems, and engineering background. In [ ], Zhou discussed the existence of solutions for a nonlinear multi-point boundary value problem of integro-differential equations of fractional order as follows: In [ ], Bai studied the existence of solutions for an impulsive fractional differential equation with nonlocal conditions in a Banach space E
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