Work

Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives

Year: 2025

Type: article

Abstract: This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler–Lagrange equation for this generalized case and providing optimality conditions for extremal curves. We explore problems with integral and holonomic constraints and consider higher-order derivatives, where the fractional orders are free.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9030188

Author: Ricardo Almeida

Institution: University of Aveiro

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Center for Research and Development in Mathematics and Applications