Homotopy perturbation pade technique for solving fractional Riccati differential equations. (English) Zbl 1401.34011

Summary: In this paper, the homotopy perturbation method (HPM) is reintroduced with the enhancement of Padé approximants to lengthen the interval of convergence of HPM when used alone in solving nonlinear problems. In this scheme, the solution takes the form of a convergent series with easily computable components. The diagonal Padé approximants are effectively used in the analysis to capture the essential behavior of the solution. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations.


34A08 Fractional ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
41A21 Padé approximation
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