Related papers: Continuous grey model with conformable fractional …
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…
In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…
Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…
In this paper an offset-free model predictive control scheme is presented for fractional-order systems using the Gr\"unwald-Letnikov derivative. The infinite-history fractional-order system is approximated by a finite-dimensional…
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…
We propose a hybrid forecast model based on discrete grey-fuzzy Markov and grey neural network model and show that our hybrid model can improve much more the performance of forecast than traditional grey-Markov model and neural network…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
Conformal prediction has become increasingly popular for quantifying the uncertainty associated with machine learning models. Recent work in graph uncertainty quantification has built upon this approach for conformal graph prediction. The…
Conformal Prediction (CP) provides distribution-free uncertainty quantification by constructing prediction sets that guarantee coverage of the true labels. This reliability makes CP valuable for high-stakes federated learning scenarios such…
The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties,…
In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
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, an adaptive fractional controller has been designed to control chaotic systems. In fact, this controller is a fractional PID controller, which the coefficients will be tuned according to a proper adaptation mechanism. The…
We consider Continuous Ordinary Differential Equations (CODE) y'=f(y), where f is a continuous function. They are known to always have solutions for a given initial condition y(0)=y0, these solutions being possibly non unique. We restrict…
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…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…
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…