The Layla and Majnun mathematical model of fractional order: Stability analysis and numerical study

In this research paper, we investigate the numerical solutions of the nonlinear complex Layla and Majnun fractional mathematical model, which describes the emotional behavior of two lovers. The fractional model is defined using the Liouville-Caputo derivative. The model is solved using a spectral collocation matrix method and a quasilinearization method with the aid of Schröder polynomials as basis functions. The existence of solutions for the model is investigated to ensure a unique solution, and a stability analysis is performed to highlight the stability regions ensuring stable solutions. In addition, the convergence analysis and error bound for the main model are illustrated in detail, and the theoretical findings are verified by several examples. The acquired results prove the ability of the proposed technique to find accurate solutions and to capture the effect of heredity of the fractional order model. The proposed techniques are proven to be effective in providing accurate solutions and can be extended to simulate similar complex problems. •Investigating the fractional order model of Layla and Majnun romantic love story.•Proving the existence of the solution to the model.•Discussing the asymptotic stability of equilibrium points in detail.•Developing a combined spectral collocation method based on the quasilinearization technique.•Utilizing the novel Schröder basis functions together with proof of convergence.