A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Lapl...

Intracellular biochemical reactions exhibit a rich dynamical phenomenology which cannot be explained within the framework of mean-field rate equations and additive noise. Here, we show that the presence of metastable states and radically different time scales are general features of a broad class of autocatalytic reaction networks, and that this fact may be exploited to gain analytical results....

‎in this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{t}^{kappa^{2}}}:=j,;;1

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...

Given an open and bounded set Ω ⊂ R , we consider the problem of minimizing the ratio between the s−perimeter and the N−dimensional Lebesgue measure among subsets of Ω. This is the nonlocal version of the well-known Cheeger problem. We prove various properties of optimal sets for this problem, as well as some equivalent formulations. In addition, the limiting behaviour of some nonlinear and non...

In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...

this work is devoted to the study of global solution for initialvalue problem of interval fractional integrodifferential equationsinvolving caputo-fabrizio fractional derivative without singularkernel admitting only the existence of a lower solution or an uppersolution. our method is based on fixed point in partially orderedsets. in this study, we guaranty the existence of special kind ofinterv...

In this paper, we investigate the longtime behavior of time fractional reaction–diffusion equations with delay. The governing partial differential equation generalizes Hutchinson, Mackey–Glass and Nicholson’s blowflies equations. Energy estimates, asymptotic stability contractivity problem are proved. finite difference technique is used to discretize time-fractional Caputo derivative, spectral ...

this paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. in this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. the robust controller is designed on the basis of fractional lyapunov stability theory. furthermore, the effects of model uncertainti...