Existence and simulation of positive solutions for m-point fractional differential equations with derivative terms

Abstract

In this article, we investigate the existence of positive solutions for a class of mm-point fractional differential equations whose nonlinear terms involve derivatives. By using the properties of the Green function and fixed point theorems, some new conditions for the existence of at least one, two, three, and 2n−12n-1 positive solutions are established. As verification, some simulation examples are given to illustrate the main results. It is worth mentioning that we study the mm-point fractional differential equations with nonlinear terms involving derivative and use the iterative method to simulate our examples and give the approximate solution.

Keywords

• fractional differential equations
• existence
• positive solution
• simulation
• 34a08
• 34b18
• 34k37