Related papers: Delay Modeling with Conformable and Caputo Derivat…
The first-order differential equation of exponential relaxation can be generalized by using either the fractional derivative in the Riemann-Liouville (R-L) sense and in the Caputo (C) sense, both of a single order less than 1. The two forms…
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…
We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.r.t time variable. First, we consider a finite difference…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
In the context of cell motility modelling and more particularly related to the Filament Based Lamelipodium Model [Manhart et al 2015 & 2017], this work deals with a rigorous mathematical proof of convergence between solutions of two…
Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is…
This article describes the fuzzy conformable fractional derivative which is based on generalized Hukuhara differentiability. On these topics, we prove a number of properties concerning this type of differentiability. In addition, fuzzy…
As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the…
Conformal Predictors (CP) are wrappers around ML models, providing error guarantees under weak assumptions on the data distribution. They are suitable for a wide range of problems, from classification and regression to anomaly detection.…
Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equation with point-wise delay or advance,…
In the theoretical research of Hepatitis B virus, mathematical models of its transmission mechanism have been thoroughly investigated, while the dynamics of the immune process in vivo have not. At present, nearly all the existing models are…
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…
In this paper, we develop two fast implicit difference schemes for solving a class of variable-coefficient time-space fractional diffusion equations with integral fractional Laplacian (IFL). The proposed schemes utilize the graded $L1$…
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the…
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the…