Existence of positive periodic solutions of some nonlinear fractional differential equations

The paper is devoted to study of existence and uniqueness of periodic solutions for a particular class of nonlinear fractional differential equations admitting its right-hand side with certain singularities. Our approach is based on Krasnosel’skiĭ and Schauder fixed point theorems and monotone itera...

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Detalles Bibliográficos
Autores: Cabada Fernández, Alberto, Kisela, Tomas
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/45457
Acceso en línea:https://hdl.handle.net/10347/45457
Access Level:acceso abierto
Palabra clave:Periodic Fractional Equation
Krasnosel’skii fixed point
Green’s function
Monotone Iterative Methods
1202 Análisis y análisis funcional
Descripción
Sumario:The paper is devoted to study of existence and uniqueness of periodic solutions for a particular class of nonlinear fractional differential equations admitting its right-hand side with certain singularities. Our approach is based on Krasnosel’skiĭ and Schauder fixed point theorems and monotone iterative technique which enable us to extend some previously known results. The discussed problems are characterized by a Green’s function which has integrable singularities disallowing a direct use of classical techniques known from theory of ordinary differential equations, therefore proper modifications are proposed. Furher, the paper presents simple numerical algorithms directly built on the iterative technique used in theoretical proofs. Illustrative examples conclude the paper.