Bernstein wavelets based numerical algorithm for solving fractional order lumpy skin disease model

Abstract Lumpy skin disease, attributed to the lumpy skin disease virus, is a viral ailment that affects cattle. This study presents a novel operational matrix employing Bernstein wavelets to examine the nonlinear dynamics of the fractional-order model of lumpy skin disease. The precise mechanism of the Riemann–Liouville arbitrary integral operator applied to Bernstein wavelets is elucidated, employing an arbitrary-order derivative in the Liouville–Caputo approach. Further, the operational matrix is employed to convert the given differential equations into a system of algebraic equations. The Adams–Bashforth–Moulton (ABM) method is also investigated as a potential solution to address the problem. A comparative analysis was performed using the ABM scheme to evaluate the precision and appropriateness of the Bernstein wavelet approach. The proposed method was validated through a convergence analysis of the Bernstein wavelet. To verify the theoretical insights and demonstrate the efficiency of the methodology, numerical simulations were ultimately performed.