Progress in Fractional Differentiation & Applications

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This paper is concerned with q-homotopy analysis transform technique to investigate system of differential equations (DE) of arbitrary order. The proposed technique describes the convergence range at large domain, by appropriate selection of initial approximation, auxiliary parameter and asymptotic parameter n (n ≥ 1). The proposed technique provides infinitely many more options for solution series and converge rapidly compared to Homotopy Analysis Method (HAM) and Homotopy Perturbation Transform Algorithm (HPTA) in same term iterations. A comparative study of suggested scheme with exact, HAM and HPTA have been done and Maple package is used to enhance the power and efficiency of proposed technique.

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