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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:
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A08 Fractional ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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