Abstract
The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.
Highlights
The fractional differential equations are models of many applications, such as medicine, engineering, physics and other sciences
Fractional impulsive differential equations played a main role in the modeling phenomena, for example in describing population dynamics which are subject to abrupt changes, as well as other phenomena such as diseases, harvesting, and so forth
There are many researchers who discussed the existence of a mild solution of impulsive fractional differential equations [11, 12, 13, 14, 15, 16, 17]
Summary
The fractional differential equations are models of many applications, such as medicine, engineering, physics and other sciences. Fractional impulsive differential equations played a main role in the modeling phenomena, for example in describing population dynamics which are subject to abrupt changes, as well as other phenomena such as diseases, harvesting, and so forth From this reason, there are many researchers who discussed the existence of a mild solution of impulsive fractional differential equations [11, 12, 13, 14, 15, 16, 17]. We will study the existence of mild solutions for considered an abstract Cauchy problem, which is entitled the impulsive nonlinear fractional order partial differential equations with nonlocal conditions, as follows:. Some of special types of cases of the proposed problem have been approached, using nonlinear functional analysis theorems and abstract Cauchy problem involving semigroup operators with Krasnoselskii's fixed point theorem, to show the solvability with some recent sufficient and necessary conditions
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