147 documents found, page 1 of 15
Fractional calculus of variations for composed functionals with generalized der...
Almeida, RicardoThis 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 integ...
On the stability of memory-dependent multi-agent systems under DoS attacks
Almeida, Ricardo; Girejko, Ewa; Machado, Luís; Malinowska, Agnieszka B.; Martins, NatáliaIn this paper, the stability analysis of memory-dependent multi-agent systems under Denial-of-Service attacks is conducted. The system under consideration is of fractional order, involving the Caputo derivative with respect to another function. Necessary and sufficient conditions for the positivity of the fractional linear system are provided. Moreover, a sufficient condition for asymptotic stability of positiv...
Fractional tempered differential equations depending on arbitrary kernels
Almeida, Ricardo; Martins, Natália; Sousa, J. Vanterler da C.In this paper, we expanded the concept of tempered fractional derivatives within both the Riemann-Liouville and Caputo frameworks, introducing a novel class of fractional operators. These operators are characterized by their dependence on a specific arbitrary smooth function. We then investigated the existence and uniqueness of solutions for a particular class of fractional differential equations, subject to sp...
An optimization condition for functionals depending on a fractional derivative ...
Almeida, RicardoIn this short communication, we will prove a necessary condition that any curve, which extremes a given class of functionals, must satisfy. In addition to the dependence on time and the unknown function, the Lagrange function depends on a fractional derivative with respect to another function, and the order of the derivative is a function of two variables, thus also depending on time.
Optimizing variational problems through weighted fractional derivatives
Almeida, RicardoIn this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with derivatives with respect to another function. Besides the fractional operators, the Lagrange function depends on extremal points. We examine the fundamental pr...
A numerical scheme for a generalized fractional derivative with variable order
Almeida, RicardoThe aim of this paper is to present an approximation formula for the Caputo fractional derivative of variable order, with dependence on an arbitrary kernel. For special cases of this kernel function, or the fractional order being constant, we recover some known formulas. This numerical method involves only integer-order derivatives, so any fractional problem can be approximated by an integer-order problem. Some...
The importance of marketing in the real estate sector
Almeida, RicardoThe real estate industry is highly competitive, and marketing can be the key to success for companies operating in this market. Marketing has stopped being an option and has become a necessity. Therefore, it is critical that companies in this industry use effective marketing strategies to stand out from their competitors. This article will discuss the importance of marketing in the real estate industry, address...
Editorial for the special issue of axioms “Calculus of variations, optimal cont...
Martins, Natália; Almeida, Ricardo; Silva, Cristiana J.; Ammi, Moulay Rchid SidiNo abstract available.
Some generalizations of the Herglotz problem involving the Mittag–Leffler tempe...
Almeida, RicardoThis paper is devoted to investigate necessary conditions of optimality for the fractional Herglotz problem, involving a general form of a tempered fractional derivative. We obtain the transversality conditions in the case of free endpoints and we study the necessary condition of optimality in the presence of higher-order derivatives.
Euler–Lagrange-type equations for functionals involving fractional operators an...
Almeida, RicardoThe 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 ¹[,], must satisfy. The Lagrange function depends on a generalized fractional derivative, on a generalized fractional integral, and on an antiderivative involving the previous fractional operators. We begin by obtaining the fractional Euler–Lagrange equation, whi...