Variational Problems Involving a Caputo-Type Fractional Derivative

2016/01/24 by Ricardo Almeida, Almeida, Ricardo · 1 citation
Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1601.07376

openalex publication_date 2016/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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 Caputo--Hadamard fractional derivatives, that are dependent on a real parameter ro. Sufficient and necessary conditions of the first and second order are presented. The cases of integral and holonomic constraints are also considered.

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