Fractal Calculus of Functions on Cantor Tartan Spaces

Abstract

In this manuscript, integrals and derivatives of functions on Cantor tartan spaces are defined. The generalisation of standard calculus, which is called F η -calculus, is utilised to obtain definitions of the integral and derivative of functions on Cantor tartan spaces of different dimensions. Differential equations involving the new derivatives are solved. Illustrative examples are presented to check the details.

Keywords

• <i>F^η</i>-calculus
• staircase function
• Cantor tartan
• fractional differential equation