Fractional spectral collocation methods for linear and nonlinear variable order FPDEs

Numerical solution of distributed order fractional differential equations by hybrid functions

The time-fractional coupled Korteweg---de Vries (KdV) system is a generalization of the classical coupled KdV system and obtained by replacing the first order time derivatives by fractional derivatives of orders $$\nu _1$$?1 and $$\nu _2$$?2, $$(0<\nu _1,\nu _2\le 1).$$(0<?1,?2≤1). In this paper, an accurate and robust numerical technique is proposed for solving the time-fractional coupled KdV equations. The shifted Legendre polynomials are introduced as basis functions of the collocation spectral method together with the operational matrix of fractional derivatives (described in the Caputo sense) in order to reduce the time-fractional coupled KdV equations into a problem consisting of a system of algebraic equations that greatly simplifies the problem. In order to test the efficiency and validity of the proposed numerical technique, we apply it to solve two numerical examples.

A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations

A study on the mild solution of impulsive fractional evolution equations

In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog. Fract. Differ. Appl. 1(2):73-85, 2015). We first derive simple and strong maximum principles for the linear fractional equation. We then implement these principles to establish uniqueness and stability results for the linear and nonlinear fractional diffusion problems and to obtain a norm estimate of the solution. In contrast with the previous results of the fractional diffusion equations, the obtained maximum principles are analogous to the ones with the Caputo fractional derivative; however, extra necessary conditions for the existence of a solution of the linear and nonlinear fractional diffusion models are imposed. These conditions affect the norm estimate of the solution as well.

/pdf/analysis-of-the-fractional-diffusion-equations-with-3l0ovw1r8m.pdf

Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel

This article is devoted to studying uniqueness of difference polynomials sharing values. The results improve those given by Liu and Yang and Heittokangas et al.

/pdf/some-results-on-difference-polynomials-sharing-values-3izr1czas9.pdf

Some results on difference polynomials sharing values

We investigate the zero distribution of -shift difference polynomials of meromorphic functions with zero order and obtain some results that extend previous results of K. Liu et al.

/pdf/value-sharing-results-for-shifts-difference-polynomials-u1g0f3k7in.pdf

Value Sharing Results for -Shifts Difference Polynomials

Abstract In this paper, we consider the existence of entire solutions of certain type of non-linear difference equation of the form: f(z)n + p(z)f(z + c)m = q(z). We also consider value distribution problems of difference polynomials of entire functions such as f(z)n(f(z)−1)f(z +c) for n = 1, which is a supplement of previous results.

Xiaoguang Qi

Papers

Some results on difference polynomials sharing values

Value Sharing Results for -Shifts Difference Polynomials

On Properties of Entire Solutions of Difference Equations and Difference Polynomials

Value distribution of difference polynomials of meromorphic functions narasimha rao. b, shilpa n. and sandeep kumar