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Progress in Fractional Differentiation & Applications

Author Country (or Countries)

Egypt

Abstract

In this work, multiple traveling wave solutions for one kind of nonlinear partial differential equations of fractional order using the tanh-function method are investigated. Namely, time fractional generalized nonlinear Huxley equation is explored. The proposed method benefits in handling other related general forms of fractional nonlinear partial differential equations. The analytic solutions behavior is illustrated graphically. In addition, a numerical treatment for the same problem is proposed using the cubic spline function method. Stability of the method is investigated based on the Von Neumann concept. The method proved to be conditionally stable. A numerical example is presented to assert that the proposed algorithm is effective. The results confirmed the effectiveness and accuracy of the proposed technique.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/070402

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