TY - JOUR AU - Castillo, René Erlín AU - Sultan, Babar PY - 2022/12/21 Y2 - 2024/03/29 TI - A derivative-type operator and its application to the solvability of a nonlinear three point boundary value problem JF - CUBO, A Mathematical Journal JA - CUBO VL - 24 IS - 3 SE - Articles DO - 10.56754/0719-0646.2403.0521 UR - https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3213 SP - 521–539 AB - <div class="page" title="Page 1"><div class="section"><div class="layoutArea"><div class="column"><p>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”.</p></div></div></div></div> ER -