TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics. In this article, we’ve constructed new traveling wave solutions including symmetrical Fibonacci function solutions, hyperbolic function solutions and rational solutions of the space-time fractional Cahn Hillihard equation D_t^α u − γD_x^α u − 6u(D_x^α u)^2 − (3u^2 − 1)D_x^α (D_x^α u) + D_x^α(D_x^α(D_x^α(D_x^α u))) = 0 and the space-time fractional symmetric regularized long wave (SRLW) equation D_t^α(D_t^α u) + D_x^α(D_x^α u) + uD_t^α(D_x^α u) + D_x^α u D_t^α u + D_t^α(D_t^α(D_x^α(D_x^α u))) = 0 via modified Kudryashov method. In addition, some of the solutions are described in the figures with the help of Mathematica.

Keywords

• Modified Kudryashov method
• fractional partial differential equations
• the space-time fractional Cahn Hillihard equation