## Articulo

• Similares en SciELO

## versión On-line ISSN 0719-0646

### Cubo vol.19 no.3 Temuco dic. 2017

#### http://dx.doi.org/10.4067/S0719-06462017000300031

Articles

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

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: acernea@fmi.unibuc.ro

Abstract

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.

Resumen

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.

References

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