Abstract
In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.
Highlights
Fractional differential equations appear naturally in a number of fields such as physics, engineering, biophysics, blood flow phenomena, aerodynamics, electron-analytical chemistry, biology, control theory, etc., An excellent account in the study of fractional differential equations can be found in [1,2,3,4,5,6,7,8,9,10,11] and references therein
Undergoing abrupt changes at certain moment of times like earthquake, harvesting, shock etc, these perturbations can be well-approximated as instantaneous change of state or impulses
These processes are modeled by impulsive differential equations
Summary
Fractional differential equations appear naturally in a number of fields such as physics, engineering, biophysics, blood flow phenomena, aerodynamics, electron-analytical chemistry, biology, control theory, etc., An excellent account in the study of fractional differential equations can be found in [1,2,3,4,5,6,7,8,9,10,11] and references therein. Undergoing abrupt changes at certain moment of times like earthquake, harvesting, shock etc, these perturbations can be well-approximated as instantaneous change of state or impulses. These processes are modeled by impulsive differential equations. Significant progress has been made in the theory of impulsive fractional differential equations [19,20,21]. We consider a class of impulsive fractional integrodifferential equations with nonlocal conditions of the form cD y t f t. Our aim is to show sufficient conditions for the existence and uniqueness of solutions of solutions to impulsive fractional integro-differential equations with nonlocal conditions
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