SciELO - Scientific Electronic Library Online

 
vol.19 número3Periodicity and stability in neutral nonlinear differential equations by Krasnoselskii’s fixed point theoremWeak homoclinic solutions to discrete nonlinear problems of Kirchhoff type with variable exponents índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google

Compartir


Cubo (Temuco)

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

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: 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.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

References

[1] R. Almeida, A. B. Malinowski and T. Odzijewicz, Fractional differential equations with dependence on the Caputo-Katugampola derivative, J. Comput. Nonlin. Dyn., 11 (2016), ID 061017, 11 pp. [ Links ]

[2] D. Băleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific, Singapore, 2012. [ Links ]

[3] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math., 90 (1988), 69-86. [ Links ]

[4] A. Cernea, On a fractional integrodifferential inclusion, Electronic J. Qual. Theory Differ. Equ., 2014 (2014), no. 25, 1-11. [ Links ]

[5] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010. [ Links ]

[6] U. N. Katugampola, A new approach to generalized fractional derivative, Bull. Math. Anal. Appl., 6 (2014) 1-15. [ Links ]

[7] A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. [ Links ]

[8] K. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. [ Links ]

[9] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego,1999. [ Links ]

[10] V. Staicu, On the solution sets to differential inclusions on unbounded interval, Proc. Edinburgh Math. Soc., 43 (2000), 475-484. [ Links ]

[11] V. Staicu, Arcwise conectedness of solution sets to differential inclusions, J. Math. Sciences 120 (2004), 1006-1015. [ Links ]

[12] S. Zeng, D. Băleanu, Y. Bai, G. Wu, Fractional differential equations of Caputo-Katugampola type and numerical solutions, Appl. Math. Comput., 315 (2017), 549-554. [ Links ]

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License