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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.19 no.3 Temuco dic. 2017 


On the solution set of a fractional integro-differential inclusion involving Caputo-Katugampola derivative

Aurelian Cernea1 

1University of Bucharest, Faculty of Mathematics and Computer Science Academiei 14, 010014 Bucharest, Romania. Academy of Romanian Scientists Splaiul Independent¸ei 54, 050094 Bucharest, Romania. E-mail:


We study an initial value problem associated to a fractional integro-differential inclusion defined by Caputo-Katugampola derivative and by a set-valued map with nonconvex values. We prove the arcwise connectedness of the solution set and that the set of selections corresponding to the solutions of the problem considered is a retract of the space of integrable functions on a given interval.

Keywords and Phrases: Differential inclusion; fractional derivative; initial value problem.


Estudiamos un problema de valor inicial asociado a la inclusión íntegro-diferencial fraccionaria definida por la derivada de Caputo-Katugampola y por una aplicación multivaluada con valores no-convexos. Demostramos la arco-conexidad del conjunto solución y que el conjunto de selecciones correspondientes a las soluciones del problema considerado es un retracto del espacio de funciones integrables en un intervalo dado.

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