Qualitative analysis of a fuzzy Volterra-Fredholm integrodifferential equation with an Atangana-Baleanu fractional derivative

Mohammed A. Almalahi; Satish K. Panchal; Fahd Jarad; Mohammed S. Abdo; Kamal Shah; Thabet Abdeljawad; Mohammed A. Almalahi; Satish K. Panchal; Fahd Jarad; Mohammed S. Abdo; Kamal Shah; Thabet Abdeljawad

doi:10.3934/math.2022876

AIMS Mathematics

2022, Volume 7, Issue 9: 15994-16016. doi: 10.3934/math.2022876

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Research article

Qualitative analysis of a fuzzy Volterra-Fredholm integrodifferential equation with an Atangana-Baleanu fractional derivative

1.
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India
2.
Department of Mathematics, Hajjah University, Hajjah, Yemen
3.
Department of Mathematics, Çankaya University, Etimesgut, Ankara, Turkey
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5.
Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen
6.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
7.
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan

Received: 18 April 2022 Revised: 15 June 2022 Accepted: 17 June 2022 Published: 30 June 2022
MSC : 34A08, 34A12, 34B15, 47H10

The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integro-differential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder's and Banach's fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.
Citation: Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad, Mohammed S. Abdo, Kamal Shah, Thabet Abdeljawad. Qualitative analysis of a fuzzy Volterra-Fredholm integrodifferential equation with an Atangana-Baleanu fractional derivative[J]. AIMS Mathematics, 2022, 7(9): 15994-16016. doi: 10.3934/math.2022876

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Abstract

The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integro-differential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder's and Banach's fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.

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