We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fra...

In this paper, we deduce a fractional-order model based on skin effect for frequency dependent transmission line model. The voltages and currents at any location in transmission line can be calculated by the proposed fractional partial differential equations. Then the fractional ordinary differential equation can obtained from the transmission line fractional partial differential equations thro...

In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising inmathematical physics with local fractional derivative operators (LFDOs). To get approximate solutionsof these equations, we utilize the reduce differential transform method (RDTM) which is basedupon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. Theobtained ...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

In this paper, we study a new operational numerical method for hybrid fuzzy fractional differential equations by using of the hybrid functions under generalized Caputo- type fuzzy fractional derivative. Solving two examples of hybrid fuzzy fractional differential equations illustrate the method.

S-asymptotically ω-periodic functions have applications to several problems, for example in the theory of functional differential equations, fractional differential equations, integral equations and partial differential equations. The concept of S-asymptotic ω-periodicity was introduced in the literature by Henrı́quez et al. 1, 2 . Since then, it attracted the attention of many researchers see 1...

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

In this paper we discuss the following problem with additive noise, \[\begin{cases} \frac{\partial^{\beta} u(t,x) }{\partial t}=-(-\triangle)^{\frac{\alpha}{2}} u(t,x)+b(u(t,x))+\sigma\dot{W}(t,x),~~t>0, \\u(0,x)=u_{0}(x),\end{cases},\] where $\alpha \in(0,2) $ and \beta \in (0,1)$, fractional time derivative is in sense of Caputo, $-(-\Delta)^{\frac{\alpha}{2}}$ Laplacian, $\sigma$ a positi...

Previous work [51] showed how to solve time-fractional diffusion equations by particle tracking. This paper extends the method to the case where the order of the fractional time derivative is greater than one. A subordination approach treats the fractional time derivative as a random time change of the corresponding Cauchy problem, with a first derivative in time. One novel feature of the time ...