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Research Article | Open Access

Controllability of fractional differential evolution equation of order γ ∈ ( 1 , 2 ) with nonlocal conditions

Sadam Hussain1, Muhammad Sarwar1( ), Kottakkaran Sooppy Nisar2( ), Kamal Shah1
Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
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Abstract

This paper investigates the existence of positive mild solutions and controllability for fractional differential evolution equations of order γ ∈ ( 1 , 2 ) with nonlocal conditions in Banach spaces. Our approach is based on Schauder's fixed point theorem, Krasnoselskii's fixed point theorem, and the Arzelà-Ascoli theorem. Finally, we include an example to verify our theoretical results.

Keywords

controllabilityfractional differential evolution equationspositive mild solutionfixed points
CLC number: 34A08, 54H25, 47H10

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 14188-14206
DOI: 10.3934/math.2023726

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Cite this article:
Hussain S, Sarwar M, Nisar KS, et al. Controllability of fractional differential evolution equation of order γ ∈ ( 1 , 2 ) with nonlocal conditions. AIMS Mathematics, 2023, 8(6): 14188-14206. https://doi.org/10.3934/math.2023726

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Received: 09 January 2023
Revised: 06 March 2023
Accepted: 09 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)