Here we state the main properties of the Caputo, Riemann-Liouville and the Caputo via Riemann-Liouville fractional derivatives and give some general notes on these properties. Some properties given in some recent literatures and used to solve fractional nonlinear partial differential equations will be proved that they are incorrect by giving some counter examples.

We investigate a nonlinear, nonlocal, and fully coupled boundary value problem containing mixed (k,ψ^)-Hilfer fractional derivative (k,ψ^)-Riemann–Liouville integral operators. Existence uniqueness results for the given are proved with aid of standard fixed point theorems. Examples illustrating main presented. The paper concludes some interesting findings.

In this article, we investigate partial integrals and derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral derivative order $\gamma = (p, q); p > 0,q 0$, functions are again corresponding to some iterated function system (IFS). Furthermore, discuss transforms

<abstract><p>In this paper, we present a general formulation of the well-known fractional drifts Riemann-Liouville type. We state main properties these integral operators. Besides, study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving operators.</p></abstract>

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several generalizations of formula for generalized functions polynomials. As a consequence, give new addition an integral representation these Finally, introduce family Lebesgue spaces show that some special belong to them.

This work investigates the existence and uniqueness of solutions for a coupled system fractional differential equations with three-point generalized integral boundary conditions within proportional derivatives Riemann-Liouville type. By using Schauder Banach fixed point theorems, we study aforesaid system. Finally, present an example to validate our theoretical outcomes.

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed functions and their properties. results directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma modified Bessel functions, some applications acquired ob...

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...

The existence and uniqueness of solutions for a coupled system Liouville–Caputo type fractional integro-differential equations with multi-point sub-strip boundary conditions are investigated in this study. contain finite number Riemann–Liouville integral non-integral nonlinearities, as well Caputo differential operators various orders subject to on an infinite interval. At the conditions, we us...