In this paper, the problem of stabilization and observer design parameter-dependent perturbed fractional-order systems is investigated. Sufficient conditions on practical Mittag–Leffler stability are given based Lyapunov technique. Firstly, using state feedback developed. Secondly, under some sufficient hypotheses, an which provides estimation constructed. Finally, numerical examples provided t...

In this work, we have studied the time fractional-order derivative of pricing European options under Heston model. We found some positivity conditions for solution obtained relative to numerical methods used. Also, thanks properties Mittag-Leffler function, were able establish a stability result solution. Some experiments are carried out confirm theoretical results obtained.

The aim of this article is to investigate a coupled hybrid system fractional differential equations with the Atangana–Baleanu–Caputo derivative which contains Mittag–Leffler kernel function in its kernel. We firstly apply Dhage fixed point principle obtain existence mild solutions. Then, we study Ulam–Hyers stability introduced system. Finally, an example presented exhibit validity our results.

To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present interest: (i) the well-scaled passage to the limit from continuous time random walk under power law assumptions to space-time fractional diffusion, (ii) the asymptotic universality of the Mittag-Leffler waiting time law in time-fractional processes, (iii) our m...

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to e...