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Fractional differential and integral equations are focus of the researchers owing to their tremendous applications in different field of science and technology, such as physics, chemistry, mathematical biology, dynamical system and engineering. In this work, a power series approach called Residual Power Series Method (RPSM) is applied for the solution of fractional (non-integer) order integro-differential equations (FIDEs). The Caputo sense is used for calculating fractional derivatives. Comparison of the obtained solution is made with the Trigonometric Transform Method (TTM) and Optimal Homotopy Asymptotic Method (OHAM). There is no restrictive condition on the proposed solution. The presented technique is simple in applicability and easily computable. [ABSTRACT FROM AUTHOR]

In this article, a semi-analytical technique called optimal homotopy asymptotic method (OHAM) is presented for numerical solutions of fractional-order integro-differential equations. The fractional-order derivatives are calculated using Caputo sense. The efficiency and reliability of proposed method is verified with multiple examples. Results of proposed method are compared with trigonometric transform method, standard least square method and perturbed least square method. The obtained results reveal that the proposed method is rapidly convergent, more reliable and easy to implement. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the implementation of the optimal homotopy asymptotic method to find the approximate solutions of two-dimensional fractional order Volterra integro-differential equations. The technique's applicability and validity are tested through some numerical examples. The fractional order derivatives are calculated using Caputo's sense. Results obtained by the proposed technique are compared with the Legendre wavelet method. The proposed method provides us with efficient and more accurate solutions than the other existing methods in the literature. Error analysis and convergence of the proposed method are also provided in the paper. [ABSTRACT FROM AUTHOR]

In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward. [ABSTRACT FROM AUTHOR]