A solving method for two-dimensional homogeneous system of fuzzy fractional differential equations

AIMS Mathematics

article

Muhammad Akram¹  Ghulam Muhammad¹  Tofigh Allahviranloo³  Ghada Ali⁴ 

[1] Department of Mathematics, University of the Punjab, New Campus;Department of Mathematics, Lahore Garrison University;Faculty of Engineering and Natural Sciences, Istinye University;Department of Mathematics, King Abdulaziz University Jeddah

关键词: system of fractional differential equations;    Mittag-Leffler function;    fuzzy fractional calculus;    Caputo fractional derivative;    diffusion process;   

DOI  :  10.3934/math.2023011

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

The purpose of this study is to extend and determine the analytical solution of a two-dimensional homogeneous system of fuzzy linear fractional differential equations with the Caputo derivative of two independent fractional orders. We extract two possible solutions to the coupled system under the definition of strongly generalized $ H $-differentiability, uncertain initial conditions and fuzzy constraint coefficients. These potential solutions are determined using the fuzzy Laplace transform. Furthermore, we extend the concept of fuzzy fractional calculus in terms of the Mittag-Leffler function involving triple series. In addition, several important concepts, facts, and relationships are derived and proved as property of boundedness. Finally, to grasp the considered approach, we solve a mathematical model of the diffusion process using proposed techniques to visualize and support theoretical results.

【 授权许可】

CC BY