... sensitivity analysis is provided in Section 9 . The optimal control approach is discussed in Section 10 . Section 11 presents the convergence analysis. Sections 12 and 13 introduce the Adams–Bashforth Moulton (ABM) method and the Runge–Kutta method, respectively, both based on the Caputo operator...

... with the Caputo operator. Findings We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models. Originality/value...