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.

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

Abstract The study presented in this article involves q -calculus connected to fractional calculus applied the univalent functions theory. Riemann-Liouville integral of -hypergeometric function is defined here, and investigations are conducted using theories differential subordination superordination. Theorems corollaries containing new superordination results proved for which best dominants su...

In this article, we investigate the analytical and approximate solutions for a fractional quadratic integral equation in frame of generalized Riemann–Liouville operator with respect to another function. The existence uniqueness results obtained. Moreover, some new special corresponding suitable values parameters ζ q are given. main proved by applying Banach’s fixed point theorem, Adomian decomp...

Abstract In this article, the notion of interval-valued preinvex functions involving Riemann–Liouville fractional integral is described. By applying this, some new refinements Hermite–Hadamard inequality for operator are presented. Some novel special cases presented results discussed as well. Also, examples to validate our results. The established outcomes article may open another direction dif...

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 give Hermite–Hadamard type inequalities of the Jensen–Mercer for Riemann–Liouville fractional integrals. We prove integral identities, and with help these identities some other eminent inequalities, such as Jensen, Hölder, power mean obtain bounds difference newly obtained inequalities.

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...

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.