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

AIMS Mathematics

article

Mohammed A. Almalahi¹  Satish K. Panchal¹  Fahd Jarad³  Mohammed S. Abdo⁵  Kamal Shah⁶  Thabet Abdeljawad⁶ 

[1] Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University;Department of Mathematics, Hajjah University;Department of Mathematics, Çankaya University;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, Hodeidah University;Department of Mathematics and Sciences, Prince Sultan University;Department of Mathematics, University of Malakand

关键词: Atangana Baleanu fractional derivative;    fractional differential equations;    fuzzy fractional derivatives;    fuzzy valued functions;    generalized Hukuhara differentiability;    fixed point theorem;   

DOI  :  10.3934/math.2022876

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY