The quantum analogs of the derivatives with respect to coordinates qk and momenta pk are commutators with operators Pk and Qk. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for an...

Integral identities created in inequality theory studies help to prove many inequalities. Recently, different fractional integral and derivative operators have been used achieve these identities. In this article, with the of Atangana-Baleanu operators, an identity was first obtained various inequalities for convex functions proved using identity. last part simulation graphs are given reveal con...

In this paper, we study the existence and uniqueness of solutions for a coupled implicit system involving ψ-Riemann–Liouville fractional derivative with nonlocal conditions. We first transformed problem into an integral then analyzed by means Banach fixed-point theorem Krasnoselskiis theorem. Some known results in literature are extended. Finally, example is given to illustrate our theoretical ...

In this paper, using the Riemann-Liouville fractional q-integral, we establish some new fractional integral inequalities by using two parameters of deformation q1 and q2.

in this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...

This paper investigates the solution to one-dimensional fractional differential equations with two types of derivative operators orders in range (1,2). Two linearized schemes numerical method are constructed. The considered FDEs equivalently transformed by Riemann–Liouville integral into their integro-partial problems reduce requirement for smoothness time. analysis stability and convergence is...

In this study, we present a new notion of nonlocal closed boundary conditions. Equipped with these conditions, discuss the existence solutions for mixed nonlinear differential equation involving right Caputo fractional derivative operator, and left Riemann–Liouville integral operators different orders. We apply decent fruitful approach fixed point theory to establish desired results. Examples a...

In this paper, we present a qualitative study of an implicit fractional differential equation involving Riemann–Liouville derivative with delay and its corresponding integral equation. Under some sufficient conditions, establish the global local existence results for that problem by applying fixed point theorems. addition, have investigated continuous integrable solutions problem. Moreover, dis...

We correct a recent result concerning the fractional derivative at extreme points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extreme points.