Related papers: An Alternative Method for Solving a Certain Class …
We derive explicit solutions for time-fractional anomalous diffusion equations with diffusivity coefficients that depend on both space and time variables. These solutions are expressed in Fox-H and generalized Wright functions, which are…
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a…
This article examines a new approach to solving ordinary differential equations based on Fractional-Calculus theory. Poisson and Sturm-Liouville-type problems are studied, together with different boundary conditions. Each case is analyzed…
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…
In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed difference method for solving two-dimensional Riesz space fractional advection-dispersion equation. The…
In this paper, we propose a new integrable fractional Fokas--Lenells equation by using the completeness of the squared eigenfunctions, dispersion relation, and inverse scattering transform. To solve this equation, we employ the…
In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time…
In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp.…
An incomplete Riemann zeta function can be expressed as a lower-bounded, improper Riemann-Liouville fractional integral, which, when evaluated at $0$, is equivalent to the complete Riemann zeta function. Solutions to Landau's problem with…
We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes the classical method of Laplace transformations…
The goal of this work is to discuss how should we impose initial values in fractional problems to ensure that they have exactly one smooth unique solution, where smooth simply means that the solution lies in a certain suitable space of…
A formal description of a functional analysis approach to the Riemann zeta-functional equation that provides in principle an infinity of different proofs based on work by the author on the existence of dilation-invariant unitary operators…
We solve a weakly singular integral equation by Laplace transformation over a finite interval of R. The equation is transformed into a Cauchy integral equation, whose resolution amounts to solving two Fredholm integral equations of the…
In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
We introduce the Nonlinear Cauchy-Riemann equations as B\"{a}cklund transformations for several nonlinear and linear partial differential equations. From these equations we treat in details the Laplace and the Liouville equations by…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We present our analytical results on the existence, uniqueness (up…
In this paper, some Ostrowski type inequalities via Riemann-Liouville fractional integrals for h-convex functions, which are super-multiplicative or super-additive, are given. These results not only generalize those of Set (2012) and Tunc…
An exponentially convergent numerical method for solving a differential equation with a right-hand fractional Riemann-Liouville time-derivative and an unbounded operator coefficient in Banach space is proposed and analysed for a…
In this study, the existence results of solution is given for fractional p-Laplacian Stum-Liouville problem for diffusion operator of order with impulsive conditions. The derivatives are described in Riemann-Liouville and Caputo sense. The…