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Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
We present a theoretical framework on non-local classical field theory using fractional integrodifferential operators. Due to the lack of easily manageable symmetries in traditional fractional calculus and the difficulties that arise in the…
This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period. The three most widely used definitions of…
Conformable fractional derivative is introduced by the authors Khalil et al. In this study we develop their concept and introduce multivariable conformable derivative for a vector valued function with several variables.
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
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…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
Historically the fractional calculus concept works an extended idea based on the question asked by Guillaume de L'H\^opital to Gottfried Wilhelm Leibniz in 1695 about the notation ${d^nf}/{dx^n}$ for the derivative operator "What if…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Conformal prediction is a powerful post-hoc framework for uncertainty quantification that provides distribution-free coverage guarantees. However, these guarantees crucially rely on the assumption of exchangeability. This assumption is…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
The time-convolutionless master equation provides a general framework to model non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann-Liouville fractional integrals, classical and Caputo fractional derivatives. Under assumptions of regularity, coercivity and…
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time…
Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…