Fractional derivatives have been around for centuries [22, 26] but recently they have found new applications in physics [2, 6, 7, 9, 15, 18, 19, 29], hydrology [1, 4, 5, 10, 14, 28], and finance [24, 25, 27]. Analytical solutions of ordinary fractional differential equations [22, 23] and partial fractional differential equations [8, 16] are now available in some special cases. But the solution ...

System identification is an important methodology used in control theory and constitutes the first step of design. It known that many real systems can be better characterized by fractional-order models. However, it often quite complex difficult to apply classical methods analytically for For this reason, integer-order models are generally considered theory. In study, alternative approximation m...

Fractional Fokker-Planck equations FFPEs have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equ...

In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order (SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbau...

The implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is employed to discretize fractional diffusion equations. The resulting systems are Toeplitz-like and then the fast Fourier transform can be used to reduce the computational cost of the matrix-vector multiplication. The preconditioned conjugate gradient normal residual method with a circula...