Gene

Extension (predicate logic)

Differential equation

Applied mathematics

Biochemistry

Computer science

Fractal

Mathematics

Exponential function

Fractal dimension

Transcription factor

Mathematical analysis

Ordinary differential equation

Repressor

Chemistry

Programming language

Partial differential equation

Operator (biology)

Fractal analysis

Fractal derivative

Fractional calculus

Alexandria Engineering Journal

In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations. As a case study, the fractal fractional Schnakenberg system is formulated with the Caputo operator (in terms of the power law), the Caputo-Fabrizio operator (with exponential decay law) and the Atangana-Baleanu fractional derivative (based on the Mittag-Liffler law). We design some algorithms for the Schnakenberg model by using the newly proposed numerical methods. In such schemes, it worth mentioning that the classical cases are recovered whenever α=1 and β=1. Numerical results obtained for different fractal-order (β∈(0,1)) and fractional-order (α∈(0,1)) are also given to address any point and query that may arise.

Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model