The Exp-function method for solving nonlinear space–time fractional differential equations in mathematical physics

Abstract

Using the Exp-function method, we derive exact solutions of the nonlinear space-time fractional Telegraph equation and space-time fractional KPP equation. As a result, we obtain many exact analytical solutions including hyperbolic function. The fractional derivative is described in Jumarie's modified Riemann-Liouville sense. This method is very effective and convenient for solving nonlinear fractional differential equations.

On One Interpolation Type Fractional Boundary-Value Problem

“…Let ξ ∈ Ξ, λ ∈ Λ, and ζ ∈ R 3 be some given vectors. Suppose that all conditions of Theorem 5 hold for the system of FDEs (24). Then, the solutions x = x(·, ξ, λ, ζ 1 ), y = y(·, ξ, λ, ζ 2 ), z = z(·, ξ, λ, ζ 3 ) of the initial-value problem (58), (45) satisfy the boundary conditions (25), if and only if…”

“…During the last few years, a number of papers devoted to the numerical-analytic methods of approximation of solutions of the fractional ordinary and partial differential equations were published. In particular, those were the well known homotopy perturbation method [12][13][14][15], Adomian's decomposition method [16][17][18][19][20][21], the variation iteration method [20,22,23], and the exp-function method [24].…”

The Traveling Wave Solutions of Space-Time Fractional Differential Equation Using Fractional Riccati Expansion Method

“…The traveling wave solution of Telegraph Equation (36) with 1 α = was derived by Wang and Li [25]. In virtue of exp-function method, many traveling wave solutions of Equation (36) was studied by Guner and Bekir [10].…”

An optimal method for approximating the delay differential equations of noninteger order

“…Fractional arithmetic and fractional differential equations appeared in many disciplines, including medicine [1], economics [2], dynamical problems [3,4], chemistry [5], mathematical physics [6], traffic model [7], fluid flow [8], and so on.…”