An approximation formula for the Katugampola integral

Abstract

The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus we convert the fractional problem into a standard one. With some examples we show the accuracy of the method, and then we present the utility of the method by solving a fractional integral equation.

This is a preprint of a paper whose final and definite form will be published in Journal of Mathematical Analysis

References in corpus (4)

• Generalized fractional calculus with applications to the calculus of variations
• Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
• Approximation of fractional integrals by means of derivatives
• Green's Theorem for Generalized Fractional Derivatives

Cited by in corpus (4)

• Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals
• New fractional integral unifying six existing fractional integrals
• Existence and Uniqueness results for a class of Generalized Fractional Differential Equations
• Theory of Nonlinear Caputo-Katugampola Fractional Differential Equations