Related papers: Overview of fractional calculus and its computer i…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.
The fractional calculus of variations is now a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. In this paper the fractional operators are defined…
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both the fundamental definitions and some of the most relevant…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the…
In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter…
Different fractional difference types of Euler-Lagrange equations are obtained within Riemann and Caputo by making use of different versions of integration by part forumlas in fractional difference calculus. An example is presented to…
The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
This paper presents a comparative study three numerical schemes such as Linear, Quadratic and Quadratic-Linear scheme for the fractional integro-differential equations defined in terms of the Caputo fractional derivatives. The error…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
A numerical scheme for solving fractional initial value problems involving the Atangana-Baleanu fractional derivative is presented. Some examples for the proposed method are included, both for equations and systems of fractional initial…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…