Corpus ID: 118631078

# Fractional Integrals and Derivatives: Theory and Applications

```@inproceedings{Samko1993FractionalIA,
title={Fractional Integrals and Derivatives: Theory and Applications},
author={Stefan Samko and Anatoly A. Kilbas and O. I. Marichev},
year={1993}
}```
• Published 1993
• Mathematics
Fractional integrals and derivatives on an interval fractional integrals and derivatives on the real axis and half-axis further properties of fractional integrals and derivatives other forms of fractional integrals and derivatives fractional integrodifferentiation of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations fo the first kind with special function kernels applications to differential equations.
6,583 Citations
The properties of Bessel-type fractional derivatives and integrals
The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axisExpand
Fractional calculus and Sinc methods
• Mathematics
• 2011
Fractional integrals, fractional derivatives, fractional integral equations, and fractional differential equations are numerically solved by Sinc methods. Sinc methods are able to deal withExpand
Some generalized fractional calculus operators and their applications in integral equations
In this paper, we survey some generalizations of fractional integrals and derivatives and present some of their properties. Using these properties, we show that many integral equations can be solvedExpand
Fractional Calculus: Integral and Differential Equations of Fractional Order
• Mathematics, Physics
• 2008
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to theExpand
Derivatives and integrals: matrix order operators as an extension of the fractional calculus
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise fromExpand
On fractional calculus with general analytic kernels
• Mathematics, Computer Science
• Appl. Math. Comput.
• 2019
This work provides a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann–Liouville fractional integral operator. Expand
FRACTIONAL VECTOR TAYLOR AND CAUCHY MEAN VALUE FORMULAS
• 2019
By defining fractional integrals and fractional derivatives along directed line segments that correspond to multivariable, we derive fractional vector Taylor formulas and fractional vector CauchyExpand
The integral analogue of the Leibniz rule for fractional calculus and its applications involving functions of several variables
• Mathematics
• 2001
Abstract The authors apply certain operators of fractional calculus (that is, integrals and derivatives of arbitrary real or complex order) with a view to evaluating various families of infiniteExpand
2 Fractional Derivatives and Differential Forms 2 . 1 Differential Forms
Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and EulerLagrange equations areExpand
Some Problems in the Theory of Integral and Differential Equations of Fractional Order
The paper is devoted to some aspects of the so-called integral and differential equations of fractional order in which an unknown function is contained under the operation of integration andExpand