Related papers: A comment on a controversial issue: a Generalized …
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
We say that an r-tuple $(g_1,...,g_r)$ of special orthogonal $d\times d$ matrices fractionally divides the $(d-1)$-dimensional sphere $S$ if there is a non-constant function in $L^2(S)$ such that its translations by $g_1,...,g_r$ sum up to…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
This paper investigates certain classes of entire functions in C^n that, together with their partial derivatives, share a finite set consisting of three elements. By employing normality criteria, we study the behaviour of such functions and…
We consider fractional differential equations of order $\alpha \in (0,1)$ for functions of one independent variable $t\in (0,\infty)$ with the Riemann-Liouville and Caputo-Dzhrbashyan fractional derivatives. A precise estimate for the order…
This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
In this work, we give the general solution sequential linear conformable fractional differential equations in the case of constant coefficients for {\alpha}(\in)(0,1]. In homogeneous case, we use a fractional exponential function which…
Aim of this paper is to study the non-existence of global solutions of the fractional differential problem involving generalized Katugampola derivative. We utilize the test function method and fractional integration by parts formula to…
In this paper we study linear and nonlinear fractional differential equations involving the Caputo fractional derivative with Mittag-Leffler non-singular kernel of order $0<\alpha<1.$ We first obtain a new estimate of the fractional…
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…
We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We state a sufficient condition for a fusion system to be saturated. This is then used to investigate localities with kernels, i.e. localities which are (in a particular way) extensions of groups by localities. As an application of these…
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…
We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value…
This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about…
The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we…
The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differential equation has a zero in a given interval of real numbers. This is a fundamental reachability problem for continuous linear dynamical systems,…
The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case…