Analyzing solution of the fractional Lorenz system and fractional Riccati equation via the modified Laplace power series residual method
Authors
A. K. Alomari
 Department of Mathematics, Faculty of Sciences, Yarmouk University, Irbid 21163, Jordan.
M. Alaroud
 Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan.
N. Tahat
 Department of Mathematics, Faculty of Science, Hashemite University, Alzarqa 13133, Jordan.
M. AlRefai
 Department of Mathematics, Faculty of Sciences, Yarmouk University, Irbid 21163, Jordan.
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 nonchaotic 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.
Share and Cite
ISRP Style
A. K. Alomari, M. Alaroud, N. Tahat, M. AlRefai, Analyzing solution of the fractional Lorenz system and fractional Riccati equation via the modified Laplace power series residual method, Journal of Mathematics and Computer Science, 37 (2025), no. 2, 154166
AMA Style
Alomari A. K., Alaroud M., Tahat N., AlRefai M., Analyzing solution of the fractional Lorenz system and fractional Riccati equation via the modified Laplace power series residual method. J Math Comput SCIJM. (2025); 37(2):154166
Chicago/Turabian Style
Alomari, A. K., Alaroud, M., Tahat, N., AlRefai, M.. "Analyzing solution of the fractional Lorenz system and fractional Riccati equation via the modified Laplace power series residual method." Journal of Mathematics and Computer Science, 37, no. 2 (2025): 154166
Keywords
 Fractional calculus
 Laplace transform
 residual power series
 multistage method
 fractional Riccati equation
 fractional chaotic system
MSC
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