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

Abstract

<abstract> <p>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.</p> </abstract>

A note on the slip effects of an Oldroyd 6-constant fluid: Optimal homotopy asymptotic method

“…This does not generally happen, especially in non-linear problems. For determining the optimal values of the convergence-control parameters, C i , i 1, 2, ..., m, one can see the [23][24][25][26][27][28][29].…”

“…The advantage of the OHAM is the integrated convergence criteria that is similar to HAM but flexible to a greater extent in implementation. Marinca et al [20][21][22] and Iqbal et al [23][24][25][26][27][28][29][30], in a series of articles, have established the validity, usefulness, simplification, and consistency of the method and acquired reliable solutions of currently significant applications in science and technology. The considered model is present in the literature [18] and has unique characteristics of earlier fluids.…”

New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2)

“…Olumide et al 18 studied the efficient result of the fractional-order SIR epidemic exemplary of childhood diseases with OHAM-2. Ahsanet al 19 presented a numerical result of a scheme of fuzzy fractional order Volterra integro-differential equation utilizing OHAM-2. Alshbool et al 20 assumed OHAM-2 to study the fractional Bernstein functioning matrices of Caputo types for resolving integro-differential equations.…”