A new efficient method for time-fractional sine-Gordon equation with the Caputo and Caputo-Fabrizio operators. (English) Zbl 1475.65158
Summary: In this work, a new efficient method called, Elzaki’s fractional decomposition method (EFDM) has been used to give an approximate series solutions to time-fractional Sine-Gordon equation. The time-fractional derivatives are described in the Caputo and Caputo-Fabrizio sense. The EFDM is based on the combination of two different methods which are: the Elzaki transform method and the Adomian decomposition method. To demonstrate the accuracy and efficiency of the proposed method, a numerical example is provided. The obtained results indicate that the EFDM is simple and practical for solving the fractional partial differential equations which appear in various fields of applied sciences.
MSC:
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35R11 | Fractional partial differential equations |
Keywords:
time-fractional sine-Gordon equation; Caputo fractional derivative operator; Caputo-Fabrizio fractional derivative operator; Elzaki transform; Adomian decomposition method; approximate series solutionReferences:
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