Controllability of fractional differential evolution equation of order $ \gamma \in (1, 2) $ with nonlocal conditions

Sadam Hussain; Muhammad Sarwar; Kottakkaran Sooppy Nisar; Kamal Shah; Sadam Hussain; Muhammad Sarwar; Kottakkaran Sooppy Nisar; Kamal Shah

doi:10.3934/math.2023726

AIMS Mathematics

2023, Volume 8, Issue 6: 14188-14206. doi: 10.3934/math.2023726

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Research article

Controllability of fractional differential evolution equation of order $ \gamma \in (1, 2) $ with nonlocal conditions

1.
Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia

Received: 09 January 2023 Revised: 06 March 2023 Accepted: 09 March 2023 Published: 17 April 2023
MSC : 34A08, 54H25, 47H10

This paper investigates the existence of positive mild solutions and controllability for fractional differential evolution equations of order $ \gamma \in (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.
- controllability,
- fractional differential evolution equations,
- positive mild solution,
- fixed points
Citation: Sadam Hussain, Muhammad Sarwar, Kottakkaran Sooppy Nisar, Kamal Shah. Controllability of fractional differential evolution equation of order $ \gamma \in (1, 2) $ with nonlocal conditions[J]. AIMS Mathematics, 2023, 8(6): 14188-14206. doi: 10.3934/math.2023726

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Abstract

This paper investigates the existence of positive mild solutions and controllability for fractional differential evolution equations of order $ \gamma \in (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.

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