In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

In this paper, we propose a numerical method to estimate the unknown order of a Riemann–Liouville fractional derivative for a fractional Stokes’ first problem for a heated generalized second grade fluid. The implicit numerical method is employed to solve the direct problem. For the inverse problem, we first obtain the fractional sensitivity equation by means of the digamma function, and then we...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

An approximate analytical solution of transient diffusion equation with space-fractional Riemann–Liouville fractional derivative has been developed. The integral-balance method and an assumed parabolic profile with undefined exponent have been used. The spatial correlation the superdiffusion coefficient in potential power-law form has been discussed. The laws of the spatial and temporal propaga...

where 2 < a, b ≤ 3, 0 < ξ1 <... < ξm <1, 0 < h1 <... < hm <1, 0 <g1 <... < gm <1, 0 < δ1 <... < δm <1, ai, bi, cj, dj Î R, f, g : [0, 1] × R 3 ® R, f, g satisfies Carathéodory conditions, Dα0+ and I α 0+ are the standard Riemann-Liouville fractional derivative and fractional integral, respectively. Wang et al. Advances in Difference Equations 2011, 2011:44 http://www.advancesindifferenceequatio...

As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...

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...

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fracti...

We investigate a nonlinear, nonlocal, and fully coupled boundary value problem containing mixed (k,ψ^)-Hilfer fractional derivative (k,ψ^)-Riemann–Liouville integral operators. Existence uniqueness results for the given are proved with aid of standard fixed point theorems. Examples illustrating main presented. The paper concludes some interesting findings.