We study calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives, with dependence on a real parameter ρ. We present sufficient and necessary conditions of first and second order to determine the extremizers of a functiona...

In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using integrals containing Mittag-Leffler functions, some well-known results for convex harmonically functions generalized. The paper connected with various published inequalities.

In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. As a second, by using this identity we obtained some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities in...

The object of this paper is to present an extension the classical Hadamard fractional integral. We will establish some new results generalized inequalities.

We begin by introducing some function spaces Lcp(R+),Xcp(J) made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties Mellin convolution operators mapping these spaces, next, derive new boundedness continuity Hadamard integral Xcp(J) Xp(J). Based this, a class boundary value problems for fractional differential equations...

This paper deals with the existence and global stability of solutions a new class Volterra partial integral equations Hadamard-Stieltjes fractional order.

We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series Sμ(r), which are expressed in terms of the Hadamard product of the generalized Mathieu series Sμ(r) and the Fox–Wright function pΨq(z). Corresponding assertions for the classical Riemann–Liouville and Erdélyi–Kober fractional integral and different...