Mediterranean Journal of Mathematics

, Volume 13, Issue 6, pp 3887–3906 | Cite as

Fractional Calculus on Fractal Interpolation for a Sequence of Data with Countable Iterated Function System

  • A. Gowrisankar
  • R. Uthayakumar


In recent years, the concept of fractal analysis is the best nonlinear tool towards understanding the complexities in nature. Especially, fractal interpolation has flexibility for approximation of nonlinear data obtained from the engineering and scientific experiments. Random fractals and attractors of some iterated function systems are more appropriate examples of the continuous everywhere and nowhere differentiable (highly irregular) functions, hence fractional calculus is a mathematical operator which best suits for analyzing such a function. The present study deals the existence of fractal interpolation function (FIF) for a sequence of data \({\{(x_n,y_n):n\geq 2\}}\) with countable iterated function system, where \({x_n}\) is a monotone and bounded sequence, \({y_n}\) is a bounded sequence. The integer order integral of FIF for sequence of data is revealed if the value of the integral is known at the initial endpoint or final endpoint. Besides, Riemann–Liouville fractional calculus of fractal interpolation function had been investigated with numerical examples for analyzing the results.


Attractor countable iterated function system fractal interpolation function fractional calculus 

Mathematics Subject Classification

28A80 26A33 41A05 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsThe Gandhigram Rural Institute, Deemed UniversityGandhigram, DindigulIndia

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