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





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”.


Fractional Derivative , boundary value problem , Hammerstein-Volterra integral equation
  • Pages: 521–539
  • Date Published: 2022-12-21
  • Vol. 24 No. 3 (2022)

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How to Cite

R. E. Castillo and B. Sultan, “A derivative-type operator and its application to the solvability of a nonlinear three point boundary value problem”, CUBO, vol. 24, no. 3, pp. 521–539, Dec. 2022.