Continuation theorem of fractional order evolutionary integral equations

  • Ahmed M. A. El-Sayed
  • Mohamed A. E. Aly


The fractional order evolutionary integral equations have been considered by the first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application.

AMS Mathematics Subject Classification

34G10 47D03 47D06 47N20 

Key words and phrases

Fractional calculus evolutionary integral equations fractional-order diffusion problem fractional-order wave problem diffusion-wave problem 


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Copyright information

© Korean Society for Computational and Applied Mathematics 2002

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAlexandria UniversityAlexandriaEgypt
  2. 2.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt

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