Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On the Operator Method for Solving Linear Integro-Differential Equations with Fractional Conformable Derivatives

Version 1 : Received: 1 August 2021 / Approved: 2 August 2021 / Online: 2 August 2021 (15:46:38 CEST)

A peer-reviewed article of this Preprint also exists.

Turmetov, B.K.; Usmanov, K.I.; Nazarova, K.Z. On the Operator Method for Solving Linear Integro-Differential Equations with Fractional Conformable Derivatives. Fractal Fract. 2021, 5, 109. Turmetov, B.K.; Usmanov, K.I.; Nazarova, K.Z. On the Operator Method for Solving Linear Integro-Differential Equations with Fractional Conformable Derivatives. Fractal Fract. 2021, 5, 109.

Journal reference: Fractal Fract. 2021, 5, 109
DOI: 10.3390/fractalfract5030109

Abstract

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

Keywords

integro-differential equation; fractional derivatives; fractional conformable derivatives; normalized systems method.

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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