We introduce stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. The fractional derivative is approximated in each sub domain using orthogonal polynomials and stability of the scheme is achieved through weakly imposed boundary and interface conditions by using a penalty term. We discuss accuracy an...

Fractional Frequency Reuse is an interference mitigation technique well suited for OFDMA system where the cell region is partitioned into two: inner cell region and outer cell region. In this paper we proposed an interference mitigation technique in LTE OFDMA femtocell system using Fractional Frequency Reuse (FFR) also system in order to improve performance of the system resource allocation is ...

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last,...

The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) stochastic (SDEs) wider class processes, including Brownian motions {BtH,t≥0} sub-fractional {ξtH,t≥0} with Hurst parameter H∈(12,1). We start by establishing the connection fPDE SDE via Feynman–Kac Theorem, which provides representation general Cauchy problem. In hindsig...

In this paper studies the exponential stability result is derived for second-order fractional stochastic integro-differential equations (FSIDEs) driven by sub-fractional Brownian motion (sub-fBm). By constructing a successive approximation method, we present pth moment of FSIDEs using analysis techniques and calculus (FC). At last, an example demonstrated to illustrate obtained theoretical resu...

The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox-Wright functions. A series expansion is also provided in order to point out the distribution of time-scales r...

The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order β ∈ (0, 1) . The fundamental solution for the Cauchy problem is interpreted as a probability density of a selfsimilar non-Markovian stochastic process related to a phenomenon of subdiffusion (the variance grows in time sub-lin...