On fractional state-dependent delay integro-differential systems under the Mittag-Leffler kernel in Banach space

M. Mallika Arjunan; Nabil Mlaiki; V. Kavitha; Thabet Abdeljawad; M. Mallika Arjunan; Nabil Mlaiki; V. Kavitha; Thabet Abdeljawad

doi:10.3934/math.2023070

AIMS Mathematics

2023, Volume 8, Issue 1: 1384-1409. doi: 10.3934/math.2023070

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On fractional state-dependent delay integro-differential systems under the Mittag-Leffler kernel in Banach space

1.
Department of Mathematics, School of Arts, Science and Humanities, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586 Saudi Arabia
3.
Department of Mathematics, School of Sciences, Arts, Media & Management, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 11 August 2022 Revised: 18 September 2022 Accepted: 21 September 2022 Published: 20 October 2022
MSC : 26A33, 34A08

The existence of Atangana-Baleanu fractional-order semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces is investigated in this paper. We establish the existence findings by using Monch's fixed point theorem and the concept of measures of non-compactness. A functioning example is provided at the end in order to illustrate the findings reached from the theoretical study.
- AB fractional-order derivative,
- mild solution,
- state-dependent delay,
- fixed point theorem (FPT)
Citation: M. Mallika Arjunan, Nabil Mlaiki, V. Kavitha, Thabet Abdeljawad. On fractional state-dependent delay integro-differential systems under the Mittag-Leffler kernel in Banach space[J]. AIMS Mathematics, 2023, 8(1): 1384-1409. doi: 10.3934/math.2023070

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Abstract

The existence of Atangana-Baleanu fractional-order semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces is investigated in this paper. We establish the existence findings by using Monch's fixed point theorem and the concept of measures of non-compactness. A functioning example is provided at the end in order to illustrate the findings reached from the theoretical study.

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