in this paper, the homotopy perturbation method (hpm) is applied to obtain an approximate solution of the fractional bratu-type equations. the convergence of the method is also studied. the fractional derivatives are described in the modied riemann-liouville sense. the results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional...

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...

Abstract: In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monot...

We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problemD0 u t μa t f t, u t , 0 < t < 1, u 0 u 1 u ′ 0 u′ 1 0, where μ > 0, a, and f are continuous, α ∈ 3, 4 is a real number, and D0 is Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to ill...

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...

In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivati...

*Correspondence: [email protected] School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P.R. China Abstract In this paper, we study the boundary value problem of a class of nonlinear fractional q-difference equations with parameter involving the Riemann-Liouville fractional derivative. By means of a fixed point theorem in cones, some positive solutions are obtained. As...

We study mixed Riemann-Liouville fractional integration operators and derivative in Marchaud form of function two variables Hölder spaces different orders each variables. The obtained are results generalized to the case with power weight.

In this paper, group analysis of the time fractional Harry-Dym equation with Riemann– Liouville derivative is performed. Its maximal symmetry group in Lie’s sense and the corresponding optimal system of subgroups are determined. Similarity reductions of the equationunder study are performed. As a result, the reduced fractional ordinary differential equations are deduced, and some group invarian...

in this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. these problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive banach space. to make the nonlinear methods work, some careful analysis of t...