Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique

Mohamed I. Abbas; Snezhana Hristova; Mohamed I. Abbas; Snezhana Hristova

doi:10.3934/math.2021740

AIMS Mathematics

2021, Volume 6, Issue 11: 12832-12844. doi: 10.3934/math.2021740

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Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique

Mohamed I. Abbas ¹,
Snezhana Hristova ^{2
,
,}

1.
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt
2.
Faculty of Mathematics and Informatics, Plovdiv University, Plovdiv 4000, Bulgaria

Received: 25 July 2021 Accepted: 27 August 2021 Published: 07 September 2021
MSC : 34A08, 34A12, 34A38

The present paper is concerned with the existence of solutions of a new class of nonlinear generalized proportional fractional differential inclusions with the right-hand side contains a Carathèodory-type multi-valued nonlinearity on infinite intervals. The investigation of the proposed inclusion problem relies on the multi-valued form of Leray-Schauder nonlinear alternative incorporated with the diagonalization technique. By specializing the parameters involved in the problem at hand, an illustrated example is proposed.
Citation: Mohamed I. Abbas, Snezhana Hristova. Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique[J]. AIMS Mathematics, 2021, 6(11): 12832-12844. doi: 10.3934/math.2021740

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Abstract

The present paper is concerned with the existence of solutions of a new class of nonlinear generalized proportional fractional differential inclusions with the right-hand side contains a Carathèodory-type multi-valued nonlinearity on infinite intervals. The investigation of the proposed inclusion problem relies on the multi-valued form of Leray-Schauder nonlinear alternative incorporated with the diagonalization technique. By specializing the parameters involved in the problem at hand, an illustrated example is proposed.

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