In [10] a “direct” stochastic transfer principle was introduced, which represented multiple integrals with respect to fractional Brownian motion in terms of multiple integrals with respect to standard Brownian motion. The method employed in [10] involved an operator Γ (n) H , mapping a class of functions LH to L 2. However, the operator does not map LH onto L 2. Hence Γ (n) H is not invertible....

For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in literature. In this regard, paper presents inequalities for operators by using a novel method based on Green’s function. Additionally, applying these identities to convex and monotone functions, new type are established. Furthermore, different form of also obtained approach. conclusio...

In this paper, we establish several necessary conditions to confirm the uniqueness-existence of solutions an extended multi-order finite-term fractional differential equation with double-order integral boundary respect asymmetric operators by relying on Banach’s fixed-point criterion. We validate our study implementing two numerical schemes handle some Riemann–Liouville value problems and obtai...

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form D ax+ f1(t, x) = v(t) + f2(t, x), lim t→a+ J1−q a x(t) = b1, where D a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville dif...

In this work, a predictor–corrector compact difference scheme for nonlinear fractional differential equation is presented. The MacCormack method provided to deal with terms, the Riemann–Liouville (R-L) integral term treated by means of second-order convolution quadrature formula, and Caputo derivative discretized L1 discrete formula. Through first second derivatives matrix under difference, we ...

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 introduce a general class of convex functions and proved some its basic properties. We establish Hermite-Hadamard type inequalities as well fractional version by using Riemann-Liouville integral operator. At the end, application to special means real numbers are also given. It can be observed from remarks given in paper that several exiting results ligature obtained immediac...

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...

In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...

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...