— This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right (Riemann-Liouville) fractional derivati...

— This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right (Riemann-Liouville) fractional derivati...

Recently, the subject of fractional differential equations has emerged as an important area of investigation. Indeed, we can find numerous applications in viscoelasticity, electrochemistry, control, electromagnetic, porous media, and so forth. In consequence, the subject of fractional differential equations is gaining much importance and attention. For some recent developments on the subject, s...

In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a steady state of the process of anomalous diffusion. The process arises from interactions within complex and non-homogeneous background. We present a numerical method which is based on the finite differences method. We co...

We formulate a fractional stochastic oscillation equation as a generalization of Bagley’s fractional differential equation. We do this in analogous way as in the case of Basset’s equation which gives rise to fractional stochastic relaxation equations. We analyze solutions under some conditions of spatial regularity of the operators considered.

in this paper two different methods are presented to approximate the solution of the fractional black-scholes equation for valuation of barrier option. also, the two schemes need less computational work in comparison with the traditional methods. in this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

This paper studies a fractional differential equation combined with Liouville–Caputo operator, namely, LCDηβ,γQ(t)=λϑ(t,Q(t)),t∈[c,d],β,γ∈(0,1],η∈[0,1], where Q(c)=qc is bounded and non-negative initial value. The function ϑ:[c,d]×R→R Lipschitz continuous in the second variable, λ>0 constant operator LCDηβ,γ convex combination of left right derivatives. We study well-posedness using fixed-po...

In this paper we study numerical methods for hybrid fuzzy fractional differential equations and the iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition. We consider a differential equation of fractional order and we compared the results with their exact solutions in order to demonstrate the validity and applicability of the method....

It is known that if a stochastic process is a solution to a classical Itô stochastic differential equation (SDE), then its transition probabilities satisfy in the weak sense the associated Cauchy problem for the forward Kolmogorov equation. The forward Kolmogorov equation is a parabolic partial differential equation with coefficients determined by the corresponding SDE. Stochastic processes whi...