Abstract
In this study, we establish some conditions for existence and uniqueness of the solutions to semilinear fractional impulsive integro-differential evolution equations with non-local conditions by using Schauder’s fixed point theorem and the contraction mapping principle.
Highlights
The topic of fractional differential equations has received a great deal of attention from many scientists and researchers during the past decades; see, for instance, [ – ]
This is mostly due to the fact that fractional calculus provides an efficient and excellent instrument to describe many practical dynamical phenomena which arise in engineering and science such as physics, chemistry, biology, economy, viscoelasticity, electrochemistry, electromagnetic, control, porous media; see [ – ]
In [ ], Balachandran et al studied the existence of solutions for fractional impulsive integrodifferential equations of the following type: CDqu(t) = A(t, u)u(t) + f u(tk) = Ik u tk, t t, u(t), h t, s, u(s) ds
Summary
The topic of fractional differential equations has received a great deal of attention from many scientists and researchers during the past decades; see, for instance, [ – ]. Many researchers study the existence of solutions for fractional differential equations; see [ – ] and the references therein. Several authors have considered a nonlocal Cauchy problem for abstract evolution differential equations having fractional order. N’Guérékata [ ] and Balachandran and Park [ ] researched the existence of solutions of fractional abstract differential equations with a nonlocal initial condition.
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