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A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…

Mathematical Physics · Physics 2009-11-10 Kathleen Cotrill-Shepherd , Mark Naber

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…

Numerical Analysis · Mathematics 2022-04-11 Kai Diethelm

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…

Other Computer Science · Computer Science 2016-11-15 Deepyaman Maiti , Ayan Acharya , R. Janarthanan , Amit Konar

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…

We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate,…

Classical Analysis and ODEs · Mathematics 2014-11-21 Douglas R. Anderson

In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…

Machine Learning · Computer Science 2019-10-01 Zhiwei Deng , Megha Nawhal , Lili Meng , Greg Mori

In this paper, Newton's law of cooling is considered from a different perspective with newly defined fractional conformable. Obtained results are compared with experimental results and found optimal fractional orders which fit better with…

Classical Physics · Physics 2018-11-12 Erdal Bas , Ramazan Ozarslan , Ahu Ercan

Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…

Numerical Analysis · Mathematics 2021-12-20 P. B. Dubovski , J. A. Slepoi

We prove that conformable ``fractional" differentiability of a function $f:[0,\infty[\,\longrightarrow \mathbb{R}$ is nothing else than the classical differentiability. More precisely, the conformable $\alpha$-derivative of $f$ at some…

Classical Analysis and ODEs · Mathematics 2024-02-12 Ahmed A. Abdelhakim , José A. Tenreiro Machado

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.

Classical Analysis and ODEs · Mathematics 2018-03-02 Nazlı Yazıcı Gözütok , Uğur Gözütok

This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…

Optimization and Control · Mathematics 2007-05-23 L. Dorcak , V. Lesko , I. Kostial

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…

High Energy Physics - Phenomenology · Physics 2010-05-28 Mathias Wagner , Andrea Walther , Bernd-Jochen Schaefer

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…

Numerical Analysis · Mathematics 2010-06-09 Brian Jain , Andrew D. Sheng

Functional Ordinary Kriging is the most widely used method to predict a curve at a given spatial point. However, uncertainty remains an open issue. In this article a distribution-free prediction method based on two different modulation…

Methodology · Statistics 2024-10-01 Anna De Magistris , Andrea Diana , Elvira Romano

This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…

Machine Learning · Statistics 2022-06-22 Zhendong Wang , Ruijiang Gao , Mingzhang Yin , Mingyuan Zhou , David M. Blei

In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…

Optimization and Control · Mathematics 2016-06-16 Pantelis Sopasakis , Haralambos Sarimveis

This study introduces a novel forecasting strategy that leverages the power of fractional differencing (FD) to capture both short- and long-term dependencies in time series data. Unlike traditional integer differencing methods, FD preserves…

Machine Learning · Computer Science 2023-12-05 Sarit Maitra , Vivek Mishra , Srashti Dwivedi , Sukanya Kundu , Goutam Kumar Kundu

The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional…

Analysis of PDEs · Mathematics 2025-12-30 Aziz El Ghazouani , Fouad Ibrahim Abdou Amir , Khoulane Mohamed , M'hamed Elomari

This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter…

Optimization and Control · Mathematics 2018-06-19 Ricardo Almeida , Dina Tavares , Delfim F. M. Torres

This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…