In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point princi...

Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives named after Riemann-Liouville, Caputo Hilfer are shown to be special cases of the earlier one. The expression for Laplace transform constructed. Inverse problems recovering space dependent time source terms a diffusion equation with involution involving considered. results on existence uniquen...

Abstract We study the optimal feedback control for fractional evolution equations with a nonlinear perturbation of time-fractional derivative term involving Caputo derivatives arbitrary kernels. Firstly, we derive mild solution in terms semigroup operator generated by resolvents and kernel from general operators establish existence uniqueness solutions systems. Then, feasible pairs applying Fil...

In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard by replacing first- and second-order time derivatives Caputo fractional of corresponding orders, Laplacian operator Sturm–Liouville defined terms right left Riemann–Liouville derivatives. Using method separation variables, derive series representations solut...

This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense. The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton iteration meth...

The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system...

In this paper, numerical solutions of the linear and nonlinear fractional integrodifferential equations with weakly singular kernel where fractional derivatives are considered in the Caputo sense, have been obtained by Legendre wavelets method. The block pulse functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration f...

In this paper, we approximate the solution to time-fractional telegraph equation by two kinds of difference methods: the Grünwald formula and Caputo fractional difference.

Necessary and sufficient stability instability conditions are reviewed extended for multi-term homogeneous linear fractional differential equations with Caputo derivatives constant coefficients. A comprehensive review of the state art regarding analysis two-term three-term fractional-order is provided, which then to case four-term equations. The properties characterized respect coefficients equ...