In this paper, we investigate a spectral Petrov-Galerkin method for an optimal control problem governed by two-sided space-fractional diffusion-advection-reaction equation. Taking into account the effect of singularities near boundary generated weak singular kernel fractional operator, establish regularity in weighted Sobolev space. Error estimates are provided presented and convergence orders ...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the use of a single fractional pole to replace the first order (singletime constant) model, which is believed to better characterize the reaction curve. Using time delayed system model with a fractional pole as the starting point, in this paper, designing fractional order cont...

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...

In this paper, we consider fractional reaction-diffusion equations with linear and nonlinear fractional reaction terms in a semi-infinite domain. Using q-Homotopy Analysis Method, solutions to these equations are obtained in the form of general recurrence relations. Closed form solutions in the form of the Mittag-Leffler function are perfectly obtained in the case with linear fractional reactio...