Abstract
Abstract Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.
Highlights
Fractional order differential equations have gained lot of attention of many researchers due to hereditary attributes and long-term memory descriptions
Many models in science and engineering such as seepage flow in porous media, anomalous diffusion, nonlinear oscillations of earthquake, fluid dynamics traffic model, electromagnetism and population dynamics are revisited in terms of fractional differential equations
Evolutionary processes that undergo abrupt change in the state either at a fixed moment of time or in a small interval of time are modeled into instantaneous impulsive evolution or noninstantaneous impulsive evolution equation, respectively
Summary
Fractional order differential equations have gained lot of attention of many researchers due to hereditary attributes and long-term memory descriptions. Due to a wide range of applications in various fields fractional order differential equations became fertile branch of Applied Mathematics. The studies of existence of mild solutions of fractional differential, integrodifferential and evolution equations using different fixed point theorems were found in [10,11,12]. Applications of the instantaneous impulsive evolution equation and existence results for integer order instantaneous impulsive evolution equations are found in [21,22,23,24]. Mild solution of noninstantaneous impulsive fractional differential equation with local initial condition has been studied by Li and Xu [33]. Meraj and Pandey [34] studied the existence of mild solutions of nonlocal semilinear evolution equation using Krasnoselskii’s fixed point theorem.
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