Results 1 to 10 of about 1,268 (147)

Analysis of hybrid fractional integro-differential equations with application to cholera dynamics [PDF]

Scientific Reports
This study establishes the existence of solutions for a class of fractional hybrid integro-differential equations governed by the $$\vartheta$$ -Caputo derivative, subject to slit-strip boundary conditions.
Mohamed S. Algolam, Mesbah Chebab, Mohammed S. Abdo, Fahdah Alshammari, Khaled Aldwoah   +4 more
doaj   +2 more sources

Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics [PDF]

Abstract and Applied Analysis, 2012
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives.
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres   +2 more
doaj   +5 more sources

Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives

Fractal and Fractional
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.
Ricardo Almeida
doaj   +3 more sources

Fractional Damping Through Restricted Calculus of Variations [PDF]

Journal of Nonlinear Science, 2021
Key words and phrases: Continuous/discrete Lagrangian and Hamiltonian modelling, fractional derivatives, fractional dissipative systems, fractional differential equations, variational principles, variational integrators. 30 pages, 7 figures. Constructive comments are welcome!!
Jiménez, Fernando, Ober-Blöbaum, Sina
openaire   +3 more sources

Minimization Problems for Functionals Depending on Generalized Proportional Fractional Derivatives

Fractal and Fractional, 2022
In this work we study variational problems, where ordinary derivatives are replaced by a generalized proportional fractional derivative. This fractional operator depends on a fixed parameter, acting as a weight over the state function and its first-order
Ricardo Almeida
doaj   +1 more source

Euler–Lagrange-Type Equations for Functionals Involving Fractional Operators and Antiderivatives

Mathematics, 2023
The goal of this paper is to present the necessary and sufficient conditions that every extremizer of a given class of functionals, defined on the set C1[a,b], must satisfy.
Ricardo Almeida
doaj   +1 more source

Optimal State Control of Fractional Order Differential Systems: The Infinite State Approach

Fractal and Fractional, 2021
Optimal control of fractional order systems is a long established domain of fractional calculus. Nevertheless, it relies on equations expressed in terms of pseudo-state variables which raise fundamental questions.
Jean-Claude Trigeassou, Nezha Maamri
doaj   +1 more source

A Stochastic Fractional Calculus with Applications to Variational Principles

Fractal and Fractional, 2020
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes.
Houssine Zine, Delfim F. M. Torres
doaj   +1 more source

Variational Problems Involving a Generalized Fractional Derivative with Dependence on the Mittag–Leffler Function

Fractal and Fractional, 2023
In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative.
Ricardo Almeida
doaj   +1 more source

Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus

Fractal and Fractional, 2020
Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations.
Arran Fernandez, Iftikhar Husain
doaj   +1 more source