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Local Fractional Calculus: a Calculus for Fractal Space-Time

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Fractals

Abstract

Recently, new notions such as local fractional derivatives and local fractional differential equations were introduced. Here we argue that these developments provide a possible calculus to deal with phenomena in fractal space-time. We show how the usual calculus is generalized to deal with non Lipschitz functions. We also indicate how a definition of a fractal measure arises from these developments much the same way as the Lebesgue measure from ordinary calculus.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India

    Kiran M. Kolwankar

  2. Department of Physics, University of Pune, 411 007, Pune, India

    Anil D. Gangal

Authors
  1. Kiran M. Kolwankar
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  2. Anil D. Gangal
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Editor information

Editors and Affiliations

  1. Faculty of Technical Mathematics aus SC, Delft University of Technology, Melalweg 4, 2628 CD, Delft, The Netherlands

    Michel Dekking

  2. INRIA, Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France

    Jacques Lévy Véhel  & Evelyne Lutton  & 

  3. Université Blaise Pascal, Département Mathématiques, 63177, Aubière Cedex, France

    Claude Tricot

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© 1999 Springer-Verlag London Limited

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Kolwankar, K.M., Gangal, A.D. (1999). Local Fractional Calculus: a Calculus for Fractal Space-Time. In: Dekking, M., Véhel, J.L., Lutton, E., Tricot, C. (eds) Fractals. Springer, London. https://doi.org/10.1007/978-1-4471-0873-3_12

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  • DOI: https://doi.org/10.1007/978-1-4471-0873-3_12

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1225-9

  • Online ISBN: 978-1-4471-0873-3

  • eBook Packages: Springer Book Archive

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