Related papers: Fractional Action-Like Variational Problems
In this paper we analyze possible extensions of the classical Steklov eigenvalue problem to the fractional setting. In particular, we find a nonlocal eigenvalue problem of fractional type that approximate, when taking a suitable limit, the…
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 develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
This paper constructs a class of non-integer dimensional continuous functions with one unbounded variation point, discusses their H\"older condition and variation on their domains. Specifically, the fractal dimension of a continuous…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
The study of fuzzy fractional variational problems in terms of a fractional Liouville-Caputo derivative is introduced. Necessary optimality conditions for problems of the fuzzy fractional calculus of variations with free end-points are…
In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…
So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well…
Singular functions and, in general, H\"older functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocity as a tool to characterize Holder and…
In this paper we deal with high-order corrections for the Fractional Derivative approach to anomalous diffusion, in super-diffusive regime, which become relevand whenever one attempts to describe the behavior of particles close to normal…
We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We…