A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The based on standard Galerkin finite element method in spatial direction, fractional Crank-Nicolson method, and extrapolation methods temporal direction. novel discrete Grönwall inequality established. Thanks inequality, error estimate of a fully obtained. Several examples are p...

The fractional calculus is one of the active research fields in mathematical analysis, primarily from its importance in modeling of various problems in engineering, physics, chemistry and other sciences. Presumably the first systematic exposition on abstract time-fractional equations with Caputo fractional derivatives is that of Bazhlekova [2]. In this fundamental work, the abstract time-fracti...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

Time fractional PDEs have been used in many applications for modeling and simulations. Many of these are multiscale contain high contrast variations the media properties. It requires very small time step size to perform detailed computations. On other hand, presence spatial grids, is required explicit methods. Explicit methods advantages as we discuss paper. In this paper, propose a partial met...

Real-time robust adaptive fuzzy fractional-order control of electrically driven flexible-joint robots has been addressed in this paper. Two important practical situations have been considered: the fact that robot actuators have limited voltage, and the fact that current signals are contaminated with noise. Through of a novel voltage-based fractional order control for an integer-order dynamical ...

The theory of fractional calculus goes back to the beginning of the theory of di erential calculus but its inherent complexity postponed the application of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of a...

We introduce a discrete-time fractional calculus of variations on the time scale hZ, h > 0. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of ...