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A new fractional analytical approach via a modified Riemann-Liouville derivative. (English) Zbl 1251.65101
Summary: This work suggests a new analytical technique called the fractional homotopy perturbation method (FHPM) for solving fractional differential equations of any fractional order. This method is based on He’s homotopy perturbation method and the modified Riemann-Liouville derivative. The fractional differential equations are described in Jumarie’s sense. The results from introducing a modified Riemann-Liouville derivative in the cases studied show the high accuracy, simplicity and efficiency of the approach.
MSC:
65L05Initial value problems for ODE (numerical methods)
34A08Fractional differential equations
34A34Nonlinear ODE and systems, general
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