 # Riemann-Liouville fractional calculus of fractal interpolation functions

2021.10.8.

"By developing our science and technology to world standards as soon as possible, the intellectuals should make a great contribution to increasing production rapidly and developing the economy."

In response to the teachings of the great leader Comrade Kim Jong Il for raising our scientific and technical level up to the world level, we have studied Riemann-Liouville fractional calcualus of fractal interpolation functions.

It is of great significance in practical applications to study fractal interpolation functions and Riemann-Liouville fractional calcualus.

Fractal interpolation functions have been powerful tools that can model objects, such as porous surfaces and seismic data, and fractional calculus have been widely applied in many areas, such as physics, biology, mechanics and finance.

Therefore, many mathematicians have been studying fractional calculus of fractal interpolation functions.

At the faculty of mathematics of Kim Il Sung University, we study Riemann-Liouville fractional calcualus of several fractal interpolation functions such as hidden variable fractal interpolation functions and hidden variable recurrent fractal interpolation functions.

We show that Riemann-Liouville fractional calcualus of hidden variable fractal interpolation functions and hidden variable recurrent fractal interpolation functions with function contractivity factors are fractal interpolation functions and estimate their box-counting dimensions.

These results were published in "Chaos, Solitons and Fractals" 140(2020) and 150(2021) under the title of "Riemann Liouville fractional integral of hidden variable interpolation function"(https://doi.org/10.1016/j.chaos.2020.110126) and "Construction of cubic spline hidden variable recurrent fractal interpolation function and its fractional calculus"(https://doi.org/10.1016/j.chaos.2021.111177), respectively.

We are going to study on fractional differential equations of fractal interpolation functions on the basis of research in fractional calculaus of hidden variable fractal interpolation function with function vertical scaling factors.