Physics

Control engineering

Nonlinear system

Pure mathematics

Calculus (dental)

Mathematics

Mathematical model

Partial differential equation

Statistics

Multivariable calculus

Engineering

Fractional calculus

Mathematical analysis

Dentistry

Quantum mechanics

Differential equation

Applied mathematics

Field (mathematics)

Ordinary differential equation

Medicine

Advances in Difference Equations

Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds. As a result, multiple innovative ideas had emerged, which caused significant divisions regarding fractional calculus in the past three years. Therefore, this work is aimed at developing a mathematical model that could be used to depict the survival of fractional calculus. Six classes are herein considered to construct a mathematical model with six ordinary differential equations. All elementary analysis have been performed. Additionally, a new analysis including strength number that accounts for the accelerative information of nonlinear and linear parts of a given epidemiological model is introduced. An analysis of the second derivative of the Lyapunov function as well as an analysis of the second derivative of each class is applied to assess how a wave could be detected. It is strongly believed that this new analysis will particularly open new doors within the field of epidemiological modelling, which will aid researchers to better understand the spread of infectious diseases. The stochastic version of the suggested model was also investigated, and numerical simulations were performed. The obtained reproductive number, strength number, extinction of criticism together with numerical simulation, revealed that the field of fractional calculus will be stable will therefore have no significant effect soon.

Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?