In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

The weak limit is derived of the sample covariance of a pair of fractionally integrated processes, one I(dY ) for −2 < dY < 12 , and the other I(1 + dX) for −2 < dX < 12 . The stochastic component (mean deviation) of the limit has the representation of a RiemannLiouville fractional integral of a functional of regular Brownian motion, B, having the form φ(t) = R t 0 XdB. In the case dX < 0, the ...

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

In the present paper certain operational formulae involving RiemannLiouville and Kober fractional q-integral operators for an analytic function are derived. The usefulness of the main results are exhibited by considering some examples which also yield q-extensions of some known results for ordinary hypergeometric functions of one and more variables.

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...

Correspondence: [email protected]. ir Department of Mathematics, Faculty of Basic Science, Babol University of Technology, Babol 47148-71167, Iran Abstract In this article, we established the existence and uniqueness of the solution for a generalized class of fractional order differential equations involving the RiemannLiouville differential operator on unbounded domain [0, +∞). The contraction ...

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 apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...