This paper is devoted to the analysis of calculation methods for solving fractional chaotic systems and impact these different approaches on behavior system. Two widely used time domain differential equations are discussed, ABM corrector-predictor method based Caputo derivative definition, long memory approach Grunwald derivative. These numerical solutions employed depict phase portrait a class...

In this article, the Tobit Kalman filtering problem is investigated for a class of discrete time-varying fractional-order systems in presence measurement censoring and stochastic nonlinearities under Round-Robin protocol (RRP). The dynamic model described by Grunwald–Letnikov difference equation, statistical means are utilized to characterize that include state-dependent disturbances as special...

Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spatial frequency domain, are the only existing methods for solving the equation. For the earth media with curved boundaries, the pseudospectral methods could be less attractive to handle the irregular computational doma...

Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...

In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this varia...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Abstract. This paper presents a step-by-step procedure for the numerical integration of fractional differential equation governing response single-degree-of-freedom (SDOF) system with derivative damping. The is developed by extending improved pseudo-force method proposed second author classical equations. To this aim, Grünwald–Letnikov approximation adopted. exploited to compute statistics SDOF...

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...