and Applied Analysis 3 Definition 2.2 see 18 . The standard Riemann-Liouville fractional derivative of order α > 0 of a continuous function y : a,∞ → R is given by D a y t 1 Γ n − α ( d dt )n ∫ t a t − s n−α−1y s ds, 2.2 where n α 1, provided that the integral on the right-hand side converges. Definition 2.3 see 18 . The Riemann-Liouville fractional integral of order α > 0 of a function y : a,∞...

Keywords: Volterra–Stieltjes integral equation Fractional integral–differential equations Riemann–Liouville fractional operators Existence and stability of solutions Fixed point a b s t r a c t Our aim in this paper is to study the existence and the stability of solutions for Riemann–Liouville Volterra–Stieltjes quadratic integral equations of fractional order. Our results are obtained by using...

In this paper, we establish some new integral inequalities for convex functions by using the Riemann-Liouville operator of non integer order. For our results some classical integral inequalities can be deduced as some special cases.

In this paper we study the existence and uniqueness of solutions of a certain Fredholm type Riemann-Liouville integral equation of two variables by using Banach contraction principle.

In this paper, we obtained some new estimates on generalization of Hadamard, Ostrowski and Simpson-like type inequalities for harmonically quasi-convex functions via Riemann Liouville fractional integral.

We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.

We compare the Riemann–Liouville fractional integral (fI) of a function f(z) with the Liouville fI of the same function and show that there are cases in which the asymptotic expansion of the former is obtained from those of the latter and the difference of the two fIs. When this happens, this fact occurs also for the fractional derivative (fD). This method is applied to the derivation of the as...

Abstract Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important study of Rosseland’s integral for stellar absorption. this paper we obtain new Milne-type inequalities, apply them to generalized Riemann–Liouville-type operators, which include most known Riemann–Liouville operators.

In this paper, we investigate some new Pólya-Szegö type integral inequalities involving the Riemann-Liouville fractional integral operator, and use them to prove some fractional integral inequalities of Chebyshev type, concerning the integral of the product of two functions and the product of two integrals. Certain special cases are also considered. Finally, examples for constructing the boundi...