International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

On the Solutions of a Class of Fractional Hyperbolic Integro-Differential Inclusions

  • Aurelian Cernea1
  1. Faculty of Mathematics and Computer Science, University of Bucharest

Abstract

We study a Darboux problem associated to a fractional hyperbolic integro-differential inclusion defined by Caputo-Katugampola fractional derivative and we prove several existence results for this problem.

How to Cite

A. Cernea, On the Solutions of a Class of Fractional Hyperbolic Integro-Differential Inclusions, Int. J. Anal. Appl. 17 (2019), 904–916. https://doi.org/10.28924/2291-8639-17-2019-904

BibTeX
@article{Cernea2019,
  author  = {Cernea, Aurelian},
  title   = {On the Solutions of a Class of Fractional Hyperbolic Integro-Differential Inclusions},
  journal = {Int. J. Anal. Appl.},
  volume  = {17},
  year    = {2019},
  pages   = {904--916},
  doi     = {10.28924/2291-8639-17-2019-904}
}

References

  • [1] R. Almeida, A. B. Malinowski and T. Odzijewicz, Fractional differential equations with dependence on the CaputoKatugampola derivative, J. Comput. Nonlinear Dyn. 11 (2016), ID 061017.
  • [2] D. B˘aleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific, Singapore, 2012.
  • [3] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86.
  • [4] A. Cernea, On an integro-differential inclusion of fractional order, Differ. Equ. Dyn. Syst. 3 (2013), 225-236.
  • [5] A. Cernea, Continuous family of solutions for fractional integro-differential inclusions of Caputo-Katugampola type, Progr. Fract. Differ. Appl. 5 (2019), 37-42.
  • [6] A. Cernea, On a fractional integro-differential inclusion of Caputo-Katugampola type, Bull. Math. Anal. Appl. to appear.
  • [7] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.
  • [8] A. Erd ´elyi and H. Kober, Some remarks on Hankel transforms, Q. J. Math. 11 (1940), 212-221.
  • [9] A. F. Filippov, Classical solutions of differential equations with multivalued right hand side, SIAM J. Control, 5 (1967), 609-621.
  • [10] U. N. Katugampola, A new approach to generalized fractional derivative, Bull. Math. Anal. Appl. 6 (2014), 1-15.
  • [11] A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [12] K. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  • [13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [14] H.D. Tuan, On local controllability of hyperbolic inclusions, J. Math. Syst. Estim. Control, 4 (1994), 319-339.
  • [15] S. Zeng, D. B˘aleanu, Y. Bai and G. Wu, Fractional differential equations of Caputo-Katugampola type and numerical solutions, Appl. Math. Comput. 315 (2017), 549-554.