A New Scheme for Solving a Fractional Differential Equation and a Chaotic System

Abstract

The subject of this study is the solution of a fractional Bernoulli equation and a chaotic system by using a novel scheme for the fractional derivative and comparison of approximate and exact solutions. It is found that the suggested method produces solutions that are identical to the exact solution. We can therefore generalize the strategy to different systems to get more accurate results. We think that the novel fractional derivative scheme that has been offered and the algorithm that has been suggested will be utilized in the future to construct and simulate a variety of fractional models that can be used to solve more difficult physics and engineering challenges.

Modeling and Analysis of a Fractional Visceral Leishmaniosis with Caputo and Caputo–Fabrizio derivatives

“…This research was carried out in the hope that it will be a useful resource for future applications and explorations of simulation by using a Caputo derivative, and to investigate new methods such as those in Refs. [18][19][20][21][22][23][24][25][26][27][28][29]…”

Neural network control of fractional-order chaotic systems with unknown control direction

“…There are three kinds of fractional derivatives that usually used in literature, namely Riemann-Liouville, Caputo, and Grünwald Letnikov fractional derivative [26] , [27] . Since the initial condition of Caputo fractional derivative is the same as that of traditional calculus and has good physical meaning, this definition will be used in this paper.…”

A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods

“…The Atangana-Baleanu fractional integral of a function y(τ) ∈ H 1 (0, c). c > 0 is as follows [42,43]:…”