Homotopy perturbation transform method for nonlinear differential equations involving to fractional operator with exponential kernel

By J. Gómez-Aguilar, Huitzilin Yépez-Martínez, J. Torres-Jiménez, T. Córdova-Fraga, R. Escobar-Jiménez, V. Olivares-Peregrino. Advances in Differential Equations, 2017

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This work presents the homotopy perturbation transform method for nonlinear fractional partial differential equations of the Caputo-Fabrizio fractional operator. Perturbative expansion polynomials are considered to obtain an infinite series solution. The effectiveness of this method is demonstrated by finding the exact solutions of the fractional equations proposed, for the special case when the limit of the integral order of the time derivative is considered.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/58f996ac3725c53d84b9559d32766148cf34d9ae