Cordial Volterra Integral Equations and Singular Fractional Integro-Differential Equations in Spaces of Analytic Functions

• Published in: Mathematical modelling and analysis Vol. 22; no. 4; pp. 548 - 567
• Main Author: Kangro, Urve
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 04.07.2017; Vilnius Gediminas Technical University
• Subjects: analytic solution; collocation method; Convergence (Mathematics); cordial integral equation; Differential equations; exponential convergence; Functions (Mathematics); Integral equations; Mathematical research; singular fractional differential equation; collocation method; singular fractional differential equation; exponential convergence; cordial integral equation; analytic solution
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/13926292.2017.1333970

We study general cordial Volterra integral equations of the second kind and certain singular fractional integro-differential equation in spaces of analytic functions. We characterize properties of the cordial Volterra integral operator in these spaces, including compactness and describe its spectrum. This enables us to obtain conditions under which these equations have a unique analytic solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.