Hilfer-type fractional differential switched inclusions with noninstantaneous impulsive and nonlocal conditions

Jinrong Wang; Ahmed Gamal Ibrahim; Donal O’regan

doi:10.15388/NA.2018.6.7

Hilfer-type fractional differential switched inclusions with noninstantaneous impulsive and nonlocal conditions

Jinrong Wang
, Ahmed Gamal Ibrahim
, Donal O’regan

Mathematics

Guizhou University
Qufu Normal University
King Faisal University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

22 Citations (Scopus)

Abstract

In this paper, we study a new class of nonlocal problems for noninstantaneous impulsive Hilfer-type fractional differential switched inclusions in Banach spaces. First, we introduce a mild solution formula for this noninstantaneous impulsive inclusion problem. Second, we show the existence of mild solutions using the Hausdorff measure of noncompactness on the space of piecewise weighted continuous functions. Finally, an example is provided to illustrate the theory.

Original language	English
Pages (from-to)	921-941
Number of pages	21
Journal	Nonlinear Analysis: Modelling and Control
Volume	23
Issue number	6
DOIs	https://doi.org/10.15388/NA.2018.6.7
Publication status	Published - 2018

Keywords

Existence
Hilfer fractional switched differential inclusions
Noninstantaneous impulsive conditions
Nonlocal conditions

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10.15388/NA.2018.6.7

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abstract = "In this paper, we study a new class of nonlocal problems for noninstantaneous impulsive Hilfer-type fractional differential switched inclusions in Banach spaces. First, we introduce a mild solution formula for this noninstantaneous impulsive inclusion problem. Second, we show the existence of mild solutions using the Hausdorff measure of noncompactness on the space of piecewise weighted continuous functions. Finally, an example is provided to illustrate the theory.",

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PY - 2018

Y1 - 2018

N2 - In this paper, we study a new class of nonlocal problems for noninstantaneous impulsive Hilfer-type fractional differential switched inclusions in Banach spaces. First, we introduce a mild solution formula for this noninstantaneous impulsive inclusion problem. Second, we show the existence of mild solutions using the Hausdorff measure of noncompactness on the space of piecewise weighted continuous functions. Finally, an example is provided to illustrate the theory.

AB - In this paper, we study a new class of nonlocal problems for noninstantaneous impulsive Hilfer-type fractional differential switched inclusions in Banach spaces. First, we introduce a mild solution formula for this noninstantaneous impulsive inclusion problem. Second, we show the existence of mild solutions using the Hausdorff measure of noncompactness on the space of piecewise weighted continuous functions. Finally, an example is provided to illustrate the theory.

KW - Existence

KW - Hilfer fractional switched differential inclusions

KW - Noninstantaneous impulsive conditions

KW - Nonlocal conditions

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DO - 10.15388/NA.2018.6.7

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JO - Nonlinear Analysis: Modelling and Control

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ER -

Hilfer-type fractional differential switched inclusions with noninstantaneous impulsive and nonlocal conditions

Abstract

Keywords

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