Solving initial and boundary value problems of fractional ordinary differential equations by using collocation and fractional powers.

[EN]This paper presents a novel approach for solving initial and boundary-values problems on ordinary fractional differential equations. The strategy considered is based on the use of a suitable truncated series expressed in terms of fractional powers of the independent variable, and a collocation a...

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Detalles Bibliográficos
Autores: Simões Patrício, M.F., Ramos Calle, Higinio, Patricio, Miguel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/157098
Acceso en línea:http://hdl.handle.net/10366/157098
Access Level:acceso abierto
Palabra clave:Caputo fractional derivative
Fractional differential equations
Gamma function
Collocation method
Initial and boundary value problems
12 Matemáticas
Descripción
Sumario:[EN]This paper presents a novel approach for solving initial and boundary-values problems on ordinary fractional differential equations. The strategy considered is based on the use of a suitable truncated series expressed in terms of fractional powers of the independent variable, and a collocation approach. With this strategy accurate numerical approximations can be obtained. The error criterion is based on the concepts of residue and relative error. Two algorithms fitted to the nature (linear or nonlinear) of the considered fractional differential equation are proposed. Finally, some problems illustrating the efficiency of the proposed method are presented.