New Solutions of the Functional Equations and Their Possible Application in Treatment of Complex Systems

  • R. R. Nigmatullin
  • B. N. Nougmanov
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 24)


In this paper we want to show some original solutions of the functional equations that can be considered as a main “bridge” connecting the fractional calculus with fractal geometry. This bridge should justify a wide application of the fractional calculus in many important applications and, from another side, increase the possibilities of the fractional geometry, when the fractional calculus is applied as a basic tool. Initially, we justify this solution and then show how it can be applied in the theory of the quasi-reproducible experiments. As an example, we chose the measurements of the corresponding voltammograms (VAGs) in electrochemistry. In the frame of new approach, one can fit the VAGs with high accuracy and prove the wide applicability of the original solution found. In the concluding section, we discuss the basic results obtained in this paper and justify their wide applicability for solution of other nontrivial problems.


Functional equations Complex systems Fractal geometry Electrochemistry Prony decomposition Intermediate model Quasy periodic measurenments Functional dispersion Self similar Special functions 


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • R. R. Nigmatullin
    • 1
  • B. N. Nougmanov
    • 2
  1. 1.Radioelectronic and Informative Measurements Technics DepartmentKazan National Research Technical University named by A.V. Tupolev (KNRTU-KAI)KazanRussian Federation
  2. 2.Physical-Mathematical Lyceum № 131KazanRussian Federation

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