Related papers: Derivatives Along a Curve and the Functional Stoch…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
A new fourth partial derivative is introduced for the study of transport dynamics. It is a Lagrangian partial derivative following the path of diffusion, not the path of convection. Use of this derivative decouples the effect of diffusion…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…
In the paper, we consider a type of stochastic differential equations driven by G-L\'evy processes. We prove that a kind of their additive functionals has path independence and extend some known results.
Analytic approximations of functions of Cayley-Dickson variables are investigated. The case of functions of complexified Cayley-Dickson variables is also encompassed. Moreover, extensions of functions of Cayley-Dickson variables are…
This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…
This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, models using different derivatives can…
The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The basic calculus rules are established and then a result derived…
Recent innovations in the differential calculus for functions of non-commuting variables, beginning with a quaternionic variable, are now extended to consider some integration.
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
We construct two bounded functional calculi for sectorial operators on Banach spaces, which enhance the functional calculus for analytic Besov functions, by extending the class of functions, generalizing and sharpening estimates, and…
In this work we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on…
The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
A new calculus based on fractal subsets of the real line is formulated. In this calculus, an integral of order $\alpha, 0 < \alpha \leq 1$, called $F^\alpha$-integral, is defined, which is suitable to integrate functions with fractal…
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…
In this paper the analogy between differential forms arising from integrals in additive calculus and forms arising from the integrals in product calculus is investigated. It is found that with an appropriate definition of scalar…