Analyzing solution of the fractional Lorenz system and fractional Riccati equation via the modified Laplace power series residual method
Year: 2024
Type: article
Abstract: The series approach is commonly used to obtain approximate analytic solutions for differential equations, but it often converges for a short time. To address this limitation, a new algorithm has been developed that enables the solution to be carried out over a longer period. The Laplace residual power series method (LRPSM) is a technique that generates a solution for fractional differential equations in terms of FOPS via simulation generalized Taylors' series in the Laplace space. To apply the LRPSM for a long time space, a new Modified LRPSM (MLRPSM) algorithm is introduced which divides the time into shorter intervals and applies the LRPSM to each interval. The algorithm investigates the continuity of the solution to ensure that the obtained solution for each interval is smoothly connected to the solution for the previous interval. The effectiveness of the proposed algorithm is demonstrated through its application to the Riccati equation and the Lorenz chaotic system. To comprehend the physical features of studied models, the 2D, and 3D graphical representations of the acquired results for some parameters had been drawn. Especially, at the critical value of the fractional derivative, which marks the transition of the solution behavior for the Lorenz system from a chaotic to a non-chaotic attractor. The efficacy, accuracy, and feasibility of this technique are verified numerically. From this viewpoint, the simulations of gained results indicate that the future iterative technique is indeed robust, effective, and convenient in gaining the approximation solutions over a longer period of a wide range of linear and nonlinear fractional physical problems.
Institutions: Yarmouk University, Amman Arab University, Hashemite University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402709060