Ghulam Farid

Opial-type inequality due to Agarwal–Pang and fractional differential inequalities

In this paper we give extensions of Opial-type integral inequalities and use them to obtain a generalization of an inequality due to Agarwal and Pang. Applications with respect to fractional derivatives and fractional integrals are also given.

Generalizations of some Integral Inequalities for Fractional Integrals

Abstract In this paper we give generalizations of the Hadamard-type inequalities for fractional integrals. As special cases we derive several Hadamard type inequalities.

Some integral inequalities for m-convex functions via generalized fractional integral operator containing generalized Mittag-Leffler function

In this paper, we are interested to prove some Hadamard and Fejér–Hadamard-type integral inequalities for m-convex functions via generalized fractional integral operator containing the generalized Mittag-Leffler function. In connection with we obtain some known results.

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.

Generalizations of some fractional integral inequalities via generalized Mittag-Leffler function

Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems. In this paper we obtain some general integral inequalities containing generalized Mittag-Leffler function and some already known integral inequalities have been produced as special cases.

Hadamard and Fejér–Hadamard inequalities for extended generalized fractional integrals involving special functions

In this paper we prove the Hadamard and the Fejér–Hadamard inequalities for the extended generalized fractional integral operator involving the extended generalized Mittag-Leffler function. The extended generalized Mittag-Leffler function includes many known special functions. We have several such inequalities corresponding to special cases of the extended generalized Mittag-Leffler function. Also there we note the known results that can be obtained.

General fractional integral inequalities for convex and m-convex functions via an extended generalized Mittag-Leffler function

In this paper some new general fractional integral inequalities for convex and m-convex functions by involving an extended Mittag-Leffler function are presented. These results produce inequalities for several kinds of fractional integral operators. Some interesting special cases of our main results are also pointed out.

On Hadamard-type inequalities for differentiable functions via Caputo k-fractional derivatives

In this paper, we prove a version of the Hadamard inequality for function f such that is convex via k-fractional Caputo derivatives. Using convexity of , we find the bounds of the difference of fractional differential inequality. Also we have found inequalities for Caputo fractional derivatives.

Straightforward Proofs of Ostrowski Inequality and Some Related Results

We give proofs of some known results in very simple and antique way. Also we find some general bounds of a nonnegative difference of the Hadamard inequality and an Ostrowski-Gruss type inequality is proved.

GENERALIZATION OF THE FEJÉR-HADAMARD`S INEQUALITY FOR CONVEX FUNCTION ON COORDINATES

In this paper, we give generalization of the Fejer-Hadamard inequality by using definition of convex functions on n-coordinates. Re- sults given in (8, 12) are particular cases of results given here.