Analysis of nonlinear implicit fractional differential equations with the Atangana-Baleanu derivative via measure of non-compactness

Kishor D. Kucche; Sagar T. Sutar; Kottakkaran Sooppy Nisar; Kishor D. Kucche; Sagar T. Sutar; Kottakkaran Sooppy Nisar

doi:10.3934/math.20241316

AIMS Mathematics

2024, Volume 9, Issue 10: 27058-27079. doi: 10.3934/math.20241316

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Analysis of nonlinear implicit fractional differential equations with the Atangana-Baleanu derivative via measure of non-compactness

1.
Department of Mathematics, Shivaji University, Kolhapur 416 004, Maharashtra, India
2.
Department of Mathematics, Dattajirao Kadam Arts, Science and Commerce College, Ichalkaranji 416115, Maharashtra, India
3.
Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, Saudi Arabia

Received: 07 June 2024 Revised: 28 July 2024 Accepted: 01 August 2024 Published: 18 September 2024
MSC : 26A33, 34A12, 47H08, 47H10

In this study, we proved existence results for nonlinear implicit fractional differential equations with the Caputo version of the Atangana-Baleanu derivative, subject to the boundary and nonlocal initial conditions. The Kuratowski's measure of non-compactness and its associated fixed point theorems–Darbo's fixed point theorem and Mönchh's fixed point theorem, are the foundation for the analysis in this paper. We support our results with examples of nonlinear implicit fractional differential equations involving the Caputo version of the Atangana-Baleanu derivative subject to both boundary and nonlocal initial conditions. In addition, we provide solutions to the problems we considered.
- implicit fractional differential equations,
- non-singular kernel,
- existence results,
- measure of non-compactness,
- fixed point theorem
Citation: Kishor D. Kucche, Sagar T. Sutar, Kottakkaran Sooppy Nisar. Analysis of nonlinear implicit fractional differential equations with the Atangana-Baleanu derivative via measure of non-compactness[J]. AIMS Mathematics, 2024, 9(10): 27058-27079. doi: 10.3934/math.20241316

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Abstract

In this study, we proved existence results for nonlinear implicit fractional differential equations with the Caputo version of the Atangana-Baleanu derivative, subject to the boundary and nonlocal initial conditions. The Kuratowski's measure of non-compactness and its associated fixed point theorems–Darbo's fixed point theorem and Mönchh's fixed point theorem, are the foundation for the analysis in this paper. We support our results with examples of nonlinear implicit fractional differential equations involving the Caputo version of the Atangana-Baleanu derivative subject to both boundary and nonlocal initial conditions. In addition, we provide solutions to the problems we considered.

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