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On the recent trends in the development, theory and applications of fractional calculus

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Fractional Calculus and Its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 457))

Abstract

As is well-known, there is a number of possibilities for the solution of the fundamental problem of fractional (integro-differential) calculus: "find the simplest common generalization of the derivation and integration processes by means of interpolation relating to the index (order) of the mentioned operations". After a brief discussion of the main directions in the development of the theory, a survey of the corresponding application topics is given (theory of functions, integral transformations, theory of approximations and summability, differential and integral equations, operator theory, generalized differentiation of discontinuous functions), particular stress being laid upon some results of the last decades.

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References

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Authors
  1. Miklós Mikolás
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Bertram Ross

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© 1975 Springer-Verlag

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Mikolás, M. (1975). On the recent trends in the development, theory and applications of fractional calculus. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067119

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  • DOI: https://doi.org/10.1007/BFb0067119

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