Abstract. We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard–Marchaud fractional derivative, is also considered. The objective is to represent these operators as series of terms involving integer-order derivatives only, and then approximate the fractional operators by a finite sum. An upper bound ...

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve different...

In this paper, we establish the existence and uniqueness result of the linear Schrodinger equation with Marchaud fractional derivative in Colombeau generalized algebra. The purpose of introducing Marchaud fractional derivative is regularizing it in Colombeau sense.

in this paper, we establish the existence and uniqueness result of the linear schrodinger equation with marchaud fractional derivative in colombeau generalized algebra. the purpose of introducing marchaud fractional derivative is regularizing it in colombeau sense.

We study mixed Riemann-Liouville fractional integration operators and derivative in Marchaud form of function two variables Hölder spaces different orders each variables. The obtained are results generalized to the case with power weight.

In this study, the variable order fractional calculus of hidden fractal interpolation function is explored. It extends constant to case order. The Riemann–Liouville and Weyl–Marchaud are investigated for function. Moreover, conditions ? on a specified range also derived. observed that, under certain conditions, again functions interpolating new data set.

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

Résumé Cette communication a pour but de proposer une généralisation de la notion de dérivée traditionnelle afin d’inclure les dérivées fractionnaires comme celles de Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud et d’autres variantes comme cas particuliers. Nous le démontrons de manière explicite pour la dérivée de Marchaud. Afin de définir cette notion il convient d’emp...