In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. As a second, by using this identity we obtained some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities in...

In this paper, a novel image denoising algorithm named fractional integral image denoising algorithm (FIIDA) is proposed, which based on fractional calculus Riemann-Liouville definition. The structures of n*n fractional integral masks of this algorithm on the directions of 135 degrees, 90 degrees, 45 degrees, 0 degrees, 180 degrees, 315 degrees, 270 degrees and 225 degrees are constructed and d...

We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1 < α ≤ 2. This operator is defined by a combination of the left and right Riemann–Liouville fractional derivatives. We stu...

We obtain a new decomposition of the Riemann–Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class Cn, n ∈ N, and allow us to develop suitable numerical approximations with known estimations for the error. The usefulness of the obtained results, in solving fractional integral equations and fractional...

In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem second-order differential equation containing fractional derivative operator. The differentiation operator was considered according to two definitions: Gerasimov-Caputo Riemann-Liouville-Visualizations eigenfunctions, biorthogonal system, distribution on real axis were present...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

We investigate compactness properties of the Riemann–Liouville operator Rα of fractional integration when regarded as operator from L2[0, 1] into C(K), the space of continuous functions over a compact subset K in [0, 1]. Of special interest are small sets K, i.e. those possessing Lebesgue measure zero (e.g. fractal sets). We prove upper estimates for the Kolmogorov numbers of Rα against certain...

In the present case, we propose novel generalized fractional integral operator describing Mittag–Leffler function in their kernel with respect to another Ф. The proposed technique is use graceful amalgamations of Riemann–Liouville (RL) and several other operators. Meanwhile, generalizations are considered order demonstrate variants involving a family positive functions n (n ∈ N) for operator. c...

The study discussed in this article is driven by the realization that many physical processes may be understood using applications of fractional operators and special functions. In study, we present examine a integral operator with an I-function its kernel. This used to solve several differential equations (FDEs). FDE has set particular cases whose solutions represent different phenomena. Many ...