Related papers: Quantitative estimates for singularity for conjuga…
We study graph-directed conjugate functional equations on the unit interval indexed by the complete digraph with self-loops on two vertices. We focus on the singularity and regularity of the solutions for compatible systems of weak…
In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider…
An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…
In this work, for an equation of high even order with a fractional derivative in the sense of Caputo, a problem is studied in a rectangular domain with conjugation conditions. A criterion for the uniqueness of a solution is given. The…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions consisting the equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our results are…
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
Criteria for piecewise linear circle homeomorphisms to be conjugate to a rigid rotation, $x\to x+\omega~({\rm mod}~1)$, with rational rotation number $\omega$ are given. The consequences of the existence of such maps in families of maps is…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
The $\alpha$-patch model is used to study aspects of fluid equations. We show that solutions of this model form singularities in finite time and give a characterization of the solution profile at the singular time.
The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems.…
We present sufficient conditions for the existence of positive solutions for a class of fractional singular boundary value problems in presence of Caputo fractional derivative. Further, the nonlinearity involved has singularity with respect…
Let $B$ be a fixed rational function of one complex variable of degree at least two. In this paper, we study solutions of the functional equation $A\circ X=X\circ B$ in rational functions $A$ and $X$. Our main result states that, unless $B$…
We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler-Lagrange type for the basic, isoperimetric, and Lagrange variational problems are…
A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…