Related papers: Introducci\'on al C\'alculo Fraccional

In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with…

The transformation property of the Caputo fractional derivative operator of a scalar function under rotation in two dimensional space is derived. The study of the transformation property is essential for the formulation of fractional…

The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known…

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.

Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications:…

We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…

A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…

Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary…

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…

This short study consists of two parts, firstly we obtain some inequalities on Caputo Fractional derivatives using the elementary inequalities. Secondly we establish several new inequalities including Caputo fractional derivatives for…

We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by…

The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the…

The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…

This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…

In this paper, we present a new derivative via the Laplace transform. The Laplace transform leads to a natural form of the fractional derivative which is equivalent to a Riemann-Liouville derivative with fixed terminal point. We first…

We begin with a brief overview of the most commonly used fractional derivatives, namely the Caputo and Riemann-Liouville derivatives. We then focus on the study of the fractional time wave equation with the Riemann-Liouville derivative,…

Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…

In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on…

We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann-Liouville fractional integrals, classical and Caputo fractional derivatives. Under assumptions of regularity, coercivity and…