Sajid Iqbal

On generalization of an integral inequality and its applications

In this paper, we give generalization of an integral inequality. We find its applications in fractional calculus by involving different kinds of fractional integral operators, for example Riemann–Liouville fractional integral, Caputo fractional derivative, Canavati fractional derivative and Widder derivative, Saigo fractional integral operator, etc.

Hardy-type inequalities for generalized fractional integral operators

Abstract The aim of this research paper is to establish the Hardy-type inequalities for Hilfer fractional derivative and generalized fractional integral involving Mittag-Leffler function in its kernel using convex and increasing functions.

On some Hardy-type inequalities for fractional calculus operators

In this article we present applications of Hardy- type and refined Hardy-type inequalities for a generalized fractional integral operator involving the Mittag-Leffler function in its kernel and for the Hilfer fractional derivative using convex and monotone convex functions.

Generalized integral inequalities for fractional calculus

In this paper, we present a variety of integral inequalities in and spaces for the integral operator involving generalized Mittag-Leffler function in its kernel, Hilfer fractional derivative, generalized Riemann-Liouville and Riemann-Liouville k-fractional integral operators.

Multiple Opial-type inequalities for general kernels with applications

The main purpose of this paper is to give the general multiple Opial-type inequalities for general kernels. We consider the monotocity and boundedness of the weight functions to prove new inequalities. As applications of our general results we establish new inequalities for Widder’s derivatives and linear differential operator. Results from [11] are obtain by applying the Canavati fractional derivatives to our main results.

On refined Hardy-type inequalities with fractional integrals and fractional derivatives

The aim of this paper is to present new more general Hardy-type inequalities for different kinds of fractional integrals and fractional derivatives.