Positive properties of the Green function for two-term fractional differential equations and its application

Abstract

In this paper, we study the positive properties of the Green function for the following two-term fractional differential equation0+ is the standard Riemann-Liouville derivative. As an application, the existence and uniqueness of positive solution are obtained under the singular conditions. Moreover, an iterative scheme is established to approximate the unique positive solution.

Meromorphic solutions of some algebraic differential equations related Painlevé equation IV and its applications

“…where c 11 = −3 4 10 + 4a 2 10 − 2b, c 12 = c 18 = 12 4 10 z 1 − 16a 2 10 z 1 − 12 3 10 11 + 12 3 10 12 + 8a 10 11 − 8a 10 12 + 8bz 1 , c 13 = c 17 = −18 4 10 z 2 1 + 24a 2 10 z 2 1 + 48 3 10 11 z 1 − 36 3 10 12 z 1 − 32a 10 11 z 1 + 24a 10 From (7), we obtain the indeterminate relations to elliptic solutions of Equation PIV with pole at z = 0:…”

“…A great deal of research has been conducted worldwide in the study of nonlinear differential equations. [1][2][3][4][5][6][7][8][9][10] The 6 Painlevé equations have been identified as the most important nonlinear ordinary differential equations ODEs. 11 In the past 2 decades, there is continuing interest in solutions of Painlevé equations.…”

Stability Analysis of Solutions for a Kind of Integro-Differential Equations with a Delay

“…Consider system (17). There are nonnegative constants , , 1 , 2 , and , positive numbers , , and 1 , and functions ( ) and ( ), such that the conditions hold:…”

“…Stability and the existence of solutions for nonlinear differential equations have been studied by many scholars [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] due to their many applications to problems in information theory, control theory, mechanics, chemistry, physics, and so on. In [5], the authors considered a second-order functional integro-differential equation with multiple delays …”

The Green’s function of a class of two-term fractional differential equation boundary value problem and its applications

“…For some recent literature on Caputo type multi-term FBVPs, we mention the papers [8,9] and the references therein. In [20], we established some new positive properties of the Green's function for the Riemann-Liouville type FBVP, in which the linear operator contains two terms:…”