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.

This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from perspective of Liu process. The class or problems considered here are differential with derivatives order β∈(1,2), 0CDtβu(t,ζ)=Au(t,ζ)+f(t,u(t,ζ))dCt+Bx(t)Cx(t)dt initial conditions u(0)=u0,u′(0)=u1, where u(t,ζ) takes values U(⊂EN),V(⊂EN) is other bounded space, and EN rep...

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.

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canoni-cal Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange form...

In this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.