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...

The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana-Baleanu fractional derivative. Since the new Atangana-Baleanu fractional derivative is non-singular and non-local, the Euler-Lagrange equations are proposed for the problems of Herglotz. Fractional variational Herglotz problems of variable order are considered and two cases are sho...

The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux consti...

Abstract: The use of the conventional advection diffusion equation in many physical situations has been questioned by many investigators in recent years and alternative diffusion models have been proposed. Fractional space derivatives are used to model anomalous diffusion or dispersion, where a particle plume spreads at a rate inconsistent with the classical Brownian motion model. When a fracti...

Abstract The fractional oscillation equation with two derivative terms in the sense of Caputo, where orders $$\alpha$$ α and $$\beta$$ β satisfy $$1&lt;\alpha \le 2$$ 1 &lt; ≤ 2 $$0&lt;\beta 1$$ <mml:mn...

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we...

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove strong necessary optimality condition of Pontryagin type. The possibility that admissible are subject to pointwise constraints is new requires more sophisticated techniques include maximality condition. start by proving results continuity solutions due needle-like pe...