相关论文: Extensions and results from a method for evaluatin…
This paper presents a novel method that allows to generalise the use of the Adam-Bashforth to Partial Differential Equations with local and non local operator. The Method derives a two step Adam-Bashforth numerical scheme in Laplace space…
Associated Legendre functions of fractional degree appear in the solution of boundary value problems in wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer,…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
A fractional generalization of the second author's higher-order diffusion theory is given and fundamental solutions are obtained. The extension from the integer to the fractional case involves a proper treatment of the fractional Laplacian…
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…
The purpose of this work is to study an approximation to an abstract Bessel-type problem, which is a generalization of the extension problem associated with fractional powers of the Laplace operator. Motivated by the success of such…
In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative…
The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation of the history of fractional calculus is presented, as well as the different attempts at fractional derivatives…
In this paper we comment the Post inversion formula for Laplace transform, and its possible application to the branch of Analytic Number theory (Arithmetical functions, RH and PNT), involving a condition in the form of iterated limit to…
We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…
This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…
We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the…
The paper presents derivation and interpretation of one type of variable order derivative definitions. For mathematical modelling of considering definition the switching and numerical scheme is given. The paper also introduces a numerical…
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…
Asymptotic expansions are obtained for contour integrals of the form \[ \int_a^b \exp \left( - zp(t) + z^{\nu /\mu } r(t) \right)q(t)dt, \] in which $z$ is a large real or complex parameter, $p(t)$, $q(t)$ and $r(t)$ are analytic functions…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
Integral representations for a complete set of linearly independent products of two solutions of the Airy equation whose arguments differ by $z_0$ are obtained using the Laplace contour integral method. This generalizes similar integral…