相关论文: A derivative concept with respect to an arbitrary …

We introduce two kinds of fractional integral operators; the one is defined via the exponential-integral function $$ E_1(x)=\int_x^\infty \frac{e^{-t}}{t}\,dt,\quad x>0, $$ and the other is defined via the special function $$…

We consider fractional Schr\"odinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragm\'en-Lindel\"of theorem for polynomially bounded…

Let E be the set of integrable and derivable causal functions of x defined on the real interval I from a to infinity, a being real, such f(a) is equal to zero for x lower than or equal to a. We give the expression of one operator that…

It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…

We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some…

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…

We consider the classical dynamics given by a one sided shift on the Bernoulli space of $d$ symbols. We study, on the space of H\"older functions, the eigendistributions of the Ruelle operator with a given potential. Our main theorem shows…

In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes…

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…

In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…

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…

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…

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…

In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…

We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional…

We prove a duality relation and an integration by parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Gronwall's inequality and continuity and differentiability…

We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall's inequality involving the power fractional…

The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…

We study the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied t^pf(t) instead of f(t) in these integrals and with parameter p a new class of…