A derivative-type operator and its application to the solvability of a nonlinear three point boundary value problem
Author
Castillo, René Erlín
Sultan, Babar
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/321310.56754/0719-0646.2403.0521
Abstract
In this paper we introduce an operator that can be thought as a derivative of variable order, i.e. the order of the derivative is a function. We prove several properties of this operator, for instance, we obtain a generalized Leibniz’s formula, Rolle and Cauchy’s mean theorems and a Taylor type polynomial. Moreover, we obtain its inverse operator. Also, with this derivative we analyze the existence of solutions of a nonlinear three-point boundary value problem of “variable order”.