A derivative-type operator and its application to the solvability of a nonlinear three point boundary value problem

René Erlín Castillo; Babar Sultan

doi:10.56754/0719-0646.2403.0521

DOI:

https://doi.org/10.56754/0719-0646.2403.0521

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”.

Keywords

Fractional Derivative , boundary value problem , Hammerstein-Volterra integral equation

René Erlín Castillo Universidad Nacional de Colombia, Departamento de Matemáticas, Bogotá, Colombia. https://orcid.org/0000-0003-1113-5827
Babar Sultan Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan. https://orcid.org/0000-0003-2833-4101

Pages: 521–539
Date Published: 2022-12-21
Vol. 24 No. 3 (2022)

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