We investigate, in the setting of sequentially complete locally convex spaces, degenerate multi-term fractional differential equations with Caputo derivatives. The obtained theoretical results are illustrated with some examples.

In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power series in the Caputo derivatives sense. To illustrate the reliability of method some examples are provided. In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power...

*Correspondence: [email protected] 1Department of Mathematical Sciences, UAE University, P.O. Box 15551, Al Ain, UAE Full list of author information is available at the end of the article Abstract In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog....

Fractional control systems with the Caputo derivative are considered. The modified controllability Gramian and the minimum energy optimal control problem are investigated. Construction of minimizing steering controls for the modified energy functional are proposed.

In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.

We prove a second Noether theorem for Lagrangian densities with fractional derivatives defined in the Riesz–Caputo sense. An application to the fractional electromagnetic field is given. AMS Subject Classifications: 49K05, 26A33.

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

We prove a Noether’s theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.

This paper presents improvements of some Opial-type inequalities involving the RiemannLiouville, Caputo and Canavati fractional derivatives, and presents some new Opial-type inequalities. Mathematics subject classification (2010): 26A33, 26D15.

In this paper, existence and uniqueness of solution to two-point boundary value for two-sided fractional differential equations involving Caputo fractional derivative is discussed, by means of the Min-Max Theorem.