In this article, we discuss the existence of solutions for a boundaryvalue problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented. 1. Formulation ...

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by Nigmatullin (1986), and Zaslavsky (1994) in R for modeling some physical phenomena. The fractional derivative models time delays in a diffusion process. We will give a survey of the recent results on the fractional Cauchy problem and its generalizati...

‎In this paper‎, ‎we introduce fractional-order into a model of HIV-1 infection of CD4^+ T--cells‎. ‎We study the effect of ‎the changing the average number of viral particles $N$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎The nonstandard finite difference (NSFD) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order HIV-1‎ ‎...

Abstract This article considers a fractional-order neuron model under an electromagnetic field in terms of generalized Caputo fractional derivatives. The motivation for incorporating derivatives the previously proposed integer-order is that impresses with efficient effects memory, and parameters orders can increase performance by amplifying degree freedom. results on uniqueness solution are est...