Related papers: Fractional Hamilton formalism within Caputo's deri…
We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing.…
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's approach of Hamiltonian formalism for…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…
In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices…
We present a general series representation formula for the local solution of Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and we present some related numerical…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when…
In the paper, a linear differential equation with variable coefficients and a Caputo fractional derivative is considered. For this equation, a Cauchy problem is studied, when an initial condition is given at an intermediate point that does…
We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem,…
Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…
This work presents an analytical and computational study of fractional-order delay differential equations formulated using both the conformable and Caputo derivatives. For the conformable case, we develop the associated integral,…
The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element.…
We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…
Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical…