Related papers: Dynamic-memory fractional calculus via generator-b…

Atangana and Baleanu proposed a new fractional derivative with non-local and no-singular Mittag-Leffler kernel to solve some problems proposed by researchers in the field of fractional calculus. This new derivative is better to describe…

In this paper we consider a modified fractional Maxwell model based on the application of Hadamard-type fractional derivatives. The model is physically motivated by the fact that we can take into account at the same time memory effects and…

We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the…

A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…

In this article, we proposed new discrete maps with memory (DMM). These maps are derived from fractional differential equations (FDE) with the Hilfer fractional derivatives of non-integer orders and periodic sequence of kicks. The suggested…

We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…

Memristors have emerged as ideal components for modeling synaptic connections in neural networks due to their ability to emulate synaptic plasticity and memory effects. Discrete models of memristor-coupled neurons are crucial for…

This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced sequence of positive operators is monotone, admits an exact…

We introduce and study the properties of a new family of fractional differential and integral operators which are based directly on an iteration process and therefore satisfy a semigroup property. We also solve some ODEs in this new model…

In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with…

The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…

Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…

This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer…

This paper provides sharp lower estimates near the origin for the functional calculus $F(-uA)$ of a generator $A$ of an operator semigroup defined on the (strictly) positive real line; here $F$ is given as the Laplace transform of a measure…

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary…

We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we…

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…

Using our recently proposed covariant algebraic approach the heat kernel for a Laplace-like differential operator in low-energy approximation is studied. Neglecting all the covariant derivatives of the gauge field strength (Yang-Mills…

Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many…

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…