Fractional Weierstrass Function by Application of Jumarie Fractional Trigonometric Functions and Its Analysis

Uttam Ghosh^1*, Susmita Sarkar², Shantanu Das³

¹Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, India.
²Department of Applied Mathematics, University of Calcutta, Kolkata, India.
³Reactor Control Systems Design Section, E & I Group, BARC, Mumbai, India.

DOI: 10.4236/apm.2015.512065                

Abstract

The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization.

Keywords

Hölder Exponent, Fractional Weierstrass Function, Box Dimension, Jumarie Fractional Derivative, Jumarie Fractional Trigonometric Function

Conflicts of Interest

The authors declare no conflicts of interest.

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