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.

In this article, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative.

We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann–Liouville fractional integrals, classical and Caputo fractional derivatives. Under assumptions of regularity, coercivity and convexity, we prove existence of solutions. AMS Subject Classifications: 26A33, 49J05.

In this paper we investigate the existence and uniqueness of solutions of a class of partial impulsive hyperbolic differential equations with fixed time impulses involving the Caputo fractional derivative. Our main tool is a fixed point theorem.

This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.

In this paper, we estimate the second and third Maclaurin's coefficients of certain subclass of bi-univalent functions in open unit disk defined by Caputo Fractional calculus operator and also indicate certain special cases.