and Applied Analysis 3 Subject to the initial condition D α−k 0 U (x, 0) = f k (x) , (k = 0, . . . , n − 1) , D α−n 0 U (x, 0) = 0, n = [α] , D k 0 U (x, 0) = g k (x) , (k = 0, . . . , n − 1) , D n 0 U (x, 0) = 0, n = [α] , (11) where ∂α/∂tα denotes the Caputo or Riemann-Liouville fraction derivative operator, f is a known function, N is the general nonlinear fractional differential operator, a...

Simpson’s rule is a numerical method used for approximating the definite integral of function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire upper and lower bounds Simpson-type inequalities means Riemann–Liouville fractional operators. We also study special cases our main results. Furthermore, give some examples with graphs to illustrate This on first pap...

This paper adopts an efficient meshless approach for approximating the nonlinear fractional fourth-order diffusion model described in Riemann–Liouville sense. A second-order difference technique is applied to discretize temporal derivatives, while radial basis function generated finite scheme approximates spatial derivatives. One key advantage of local collocation method approximation derivativ...

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.

It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further definition based on Mellin transform and it can be used when applied to radial functions. The main finding tested case space-fractional diffusion equation. one-dimensional also considered, such Riesz (namely symmetric Riesz–Feller) derivative established. This ...

The fractional variational calculus is a recent fifield, where classical problems are considered, but in the presence of derivatives. Since there several defifinitions derivatives, it logical to think different types optimality conditions. For this reason, order solve problems, two theorems necessary conditions well known: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville o...

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

We study the existence and monotone iterative approximation of mild solutions fractional-order neutral differential equations involving a generalized fractional derivative order 0 < α 1 which can be reduced to Riemann–Liouville or Hadamard derivatives. The is obtained via fixed point techniq...