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Fractional Cauchy Problems for Infinite Interval Case-II

Author

Listed:
  • Mohammed Al Horani

    (Department of Mathematics, The University of Jordan, Amman 11942, Jordan)

  • Mauro Fabrizio

    (Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy)

  • Angelo Favini

    (Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy)

  • Hiroki Tanabe

    (Takarazuka, Hirai Sanso 12-13, Osaka 665-0817, Japan)

Abstract

We consider fractional abstract Cauchy problems on infinite intervals. A fractional abstract Cauchy problem for possibly degenerate equations in Banach spaces is considered. This form of degeneration may be strong and some convenient assumptions about the involved operators are required to handle the direct problem. Required conditions on spaces are also given, guaranteeing the existence and uniqueness of solutions. The fractional powers of the involved operator B X have been investigated in the space which consists of continuous functions u on [ 0 , ∞ ) without assuming u ( 0 ) = 0 . This enables us to refine some previous results and obtain the required abstract results when the operator B X is not necessarily densely defined.

Suggested Citation

  • Mohammed Al Horani & Mauro Fabrizio & Angelo Favini & Hiroki Tanabe, 2019. "Fractional Cauchy Problems for Infinite Interval Case-II," Mathematics, MDPI, vol. 7(12), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1165-:d:293219
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