Results in Mathematics

, Volume 65, Issue 1, pp 67–79

Ulam–Hyers Stability for the Darboux Problem for Partial Fractional Differential and Integro-differential Equations via Picard Operators


DOI: 10.1007/s00025-013-0330-x

Cite this article as:
Abbas, S. & Benchohra, M. Results. Math. (2014) 65: 67. doi:10.1007/s00025-013-0330-x


In the present paper we investigate some uniqueness and Ulam’s type stability concepts of fixed point equations due to Rus, for the Darboux problem of partial differential and integro-differential equations involving the Caputo fractional derivative. Our results are obtained by using weakly Picard operators theory.

Mathematics Subject Classification

26A33 34G20 34A40 45N05 47H10 


Fractional differential equation integro-differential equation left-sided mixed Riemann-Liouville integral Caputo fractional order derivative Darboux problem weekly Picard operator fixed point equation Ulam–Hyers stability 

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.MontrealCanada
  2. 2.Laboratoire de MathématiquesUniversité de Sidi Bel-AbbèsSidi Bel-AbbèsAlgeria

Personalised recommendations