2018
DOI: 10.1007/978-3-030-02155-9_16
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Existence Results for an Impulsive Fractional Integro-Differential Equations with a Non-compact Semigroup

Abstract: In this paper we study a fractional differential equations problem with not instantaneous impulses involving a non-compact semigroup. We present some concepts and facts about the strongly continuous semigroup and the measure of noncompactness. After that we give an existence theorem of our problem using a condensing operator and the measure of noncompactness.

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Cited by 16 publications
(11 citation statements)
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“…Fractional differential equations are relevant in many fields of science, such as chemistry, fluid systems, and electromagnetic; for more details about the theory of fractional differential equations and their applications, we invite the readers to see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein. Some physical applications of fractional differential equations include viscoelasticity, Schrodinger equation, fractional diffusion equation, and fractional relaxation equation; for more details, we refer the readers to [17].…”
Section: Introductionmentioning
confidence: 99%
“…Fractional differential equations are relevant in many fields of science, such as chemistry, fluid systems, and electromagnetic; for more details about the theory of fractional differential equations and their applications, we invite the readers to see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein. Some physical applications of fractional differential equations include viscoelasticity, Schrodinger equation, fractional diffusion equation, and fractional relaxation equation; for more details, we refer the readers to [17].…”
Section: Introductionmentioning
confidence: 99%
“…Some physical problems have sudden changes and discontinuous jumps. To model these problems, we impose impulsive conditions on the differential equations at discontinuity points; for more details about impulsive fractional differential equations, we give the following references [7][8][9][10][11][12][13].…”
Section: Introductionmentioning
confidence: 99%
“…Several researchers in the recent years have employed the fractional calculus as a way of describing natural phenomena in different fields such as physics, biology, finance, economics, and bioengineering (for more details see [1][2][3][4][5][6][7][8][9] and many other references).…”
Section: Introductionmentioning
confidence: 99%