in this paper, exp-function and (g′/g)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. as a results, some new exact traveling wave solutions are obtained.

In this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for α ∈ (0 , 1] and in case 2, we use the right Riemann-Liouville fractional derivatives on R+, for α ∈ (1 , +∞). The exact solutions are obtained for the both cases by Laplace transforms and stable sub...

This paper discuss the longstanding problems of fractional calculus such as too many definitions while lacking physical or geometrical meanings, and try to extend fractional calculus to any dimension. First, some different definitions of fractional derivatives, such as the Riemann-Liouville derivative, the Caputo derivative, Kolwankar’s local derivative and Jumarie’s modified Riemann-Liouville ...

In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liou...

In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to non-symmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space H α/2 0 (0, 1) but the ...

We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann–Liouville fractional derivatives and integrals in the sense of Jumarie. The main results provide fractional versions of the theorems of Green and Gauss, fractional Euler–Lagrange equations, and fractional natural boundary conditions. As an application we discuss...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

This study, considers the fractional order cable model (FCM) in sense of Riemann–Liouville derivatives (R-LFD). We use a modified implicit finite difference approximation to solve FCM numerically. The Fourier series approach is used examine proposed scheme’s theoretical analysis, including stability and convergence. scheme shown be unconditionally stable, approximate solution converges exact so...

Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables. The Gramian is generalized and steering functions between memory values are characterized.