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Decomposition method for solving fractional Riccati differential equations. (English) Zbl 1107.65121
Summary: We implement a relatively new analytical technique, the Adomian decomposition method, for solving fractional Riccati differential equations. The fractional derivatives are described in the Caputo sense. 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. Some numerical examples are presented to illustrate the efficiency and reliability of the method.
MSC:
65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations
26A33Fractional derivatives and integrals (real functions)