Fractional differential equations through Laguerre expansions in abstract spaces: error estimates

Abstract

An approximation procedure by the means of expansion with respect to Laguerre orthogonal basis of the space is given. It is applied to solutions of a class of convolution equations, by transforming them to corresponding systems of algebraic equations for the coefficients. Especially, Volterra-type integral and integro-differential equations and system of equations with fractional derivatives modeling viscoelastic rod are solved. Error estimates depending on the order of approximation are derived.

Keywords:

• Abel–Volterra integral equations
• Tempered distributions
• Approximation of tempered convolution
• Laguerre polynomials
• Error estimate
• Fractional differential equations
• Class of fractional equations in mechanics

Acknowledgements

This article is suppored by project MNTS.