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Fractional Differential Equations: A Emergent Field in Applied and Mathematical Sciences

In: Factorization, Singular Operators and Related Problems

Author

Listed:
  • Anatoly A. Kilbas

    (Belarusian State University)

  • Hari M. Srivastava

    (University of Victoria)

  • Juan J. Trujillo

    (University of La Laguna)

Abstract

The paper is devoted to some aspects of differential equations of fractional order and their applications. It is explained a fact that the subject of fractional differential equations is an emergent topic as a very useful tool to model many anomalous phenomena in nature and in the theory of complexity systems. Various fractional integral and fractional derivative are presented together with some of their properties. Simple partial differential equations are discussed in connection with anomalous diffusion. A new model, useful in both sub-diffusion and super-fast diffusion processes, is introduced. Such a model, generalizing the clasical problem associated with the heat equation, involves the generalized Liouville fractional derivative over the time variable. The one-dimensional case is studied and explicitely solved, and its generalization to the multi-dimensional case is discussed.

Suggested Citation

  • Anatoly A. Kilbas & Hari M. Srivastava & Juan J. Trujillo, 2003. "Fractional Differential Equations: A Emergent Field in Applied and Mathematical Sciences," Springer Books, in: Stefan Samko & Amarino Lebre & António F. dos Santos (ed.), Factorization, Singular Operators and Related Problems, pages 151-173, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0227-0_11
    DOI: 10.1007/978-94-017-0227-0_11
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