Numerical solution of system of fuzzy fractional order Volterra integro-differential equation using optimal homotopy asymptotic method

AIMS Mathematics

article

Sumbal Ahsan¹  Rashid Nawaz¹  Muhammad Akbar¹  Saleem Abdullah¹  Kottakkaran Sooppy Nisar²  Velusamy Vijayakumar³ 

[1] Department of Mathematics, Abdul Wali Khan University Mardan;Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University;Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology

关键词: OHAM;    fuzzy Caputo operator;    Riemann-Liouville fractional integral operator;    approximate solution;    system of fuzzy fractional order;    Volterra integro-differential equations;   

DOI  :  10.3934/math.2022726

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, an efficient technique called Optimal Homotopy Asymptotic Method has been extended for the first time to the solution of the system of fuzzy integro-differential equations of fractional order. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The fuzzy fractional derivatives are defined in Caputo sense. It is followed by suggesting a new result from Optimal Homotopy Asymptotic Method for Caputo fuzzy fractional derivative. We then construct a detailed procedure on finding the solutions of system of fuzzy integro-differential equations of fractional order and finally, we demonstrate a numerical example. The validity and efficiency of the proposed technique are demonstrated via these numerical examples which depend upon the parametric form of the fuzzy number. The optimum values of convergence control parameters are calculated using the well-known method of least squares, obtained results are compared with fractional residual power series method. It is observed from the results that the suggested method is accurate, straightforward and convenient for solving system of fuzzy Volterra integrodifferential equations of fractional order.

【 授权许可】

CC BY