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

• Autores: René Erlín Castillo, Babar Sultan
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 3, 2022, págs. 521-539
• Idioma: inglés
• DOI: 10.56754/0719-0646.2403.0521
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este artículo introducimos un operador que puede ser pensado como una derivada de orden variable, i.e. el orden de la derivada es una función. Demostramos varias propiedades de este operador, por ejemplo, obtenemos una fórmula generalizada de Leibniz, teoremas de valor medio de Rolle y Cauchy y un polinomio de tipo Taylor. Más aún, obtenemos su operador inverso. También con esta derivada analizamos la existencia de soluciones de un problema no lineal de valor en la frontera de tres puntos de “orden variable”.

  • English

    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”.

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