In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM). The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.
The paper must have abstract. In this paper, we present an approximate analytical algorithm to solve non-linear quadratic Riccati differential equations of fractional order based on the optimal homotopy asymptotic method (OHAM). OHAM has the benefit of adjusting the convergence rate and the region of the solution series via several auxiliary parameters over the homotopy analysis method (HAM) that has only one auxiliary parameter. The proposed algorithm is applied to initial value problems of the fractional order Riccati equations employing both non-integer and integer derivatives. Additionally, our proposed algorithm outcomes are compared against the Adams-Bashforth-Moulton numerical method (ABFMM) and other well-known analytical methods.
The aim of this paper is to obtain an approximate analytical solution of the fractional order logistic equation using the optimal homotopy asymptotic method (OHAM).OHAM uses optimally determined auxiliary constants to control and adjust the convergence of the series solution. We apply OHAM to the fractional order logistic equation for noninteger and integer derivatives. Additionally, we compare its performance with that of the Adams-Bashforth-Moulton method (ABFMM).
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