In providing an accurate approximate analytical solution to the non-linear system of fractional-order susceptible-infected-recovered epidemic model (FOSIREM) of childhood disease has been a challenge because no norm guarantees the convergence of the infinite series solution. We compute an accurate approximate analytical solution using the optimal homotopy asymptotic method (OHAM). The fractional differential equations operator (FDEO) is given as conformable derivative operator (CDO). We show the basic idea of the proposed method, the CDO sense, equilibrium points, local asymptotic stability, reproduction number, and the convergence analysis of the proposed method. Numerical results and comparisons with other approximate analytical solutions are given to validate the efficiency of the method. The proposed method speedily converges to the exact solution as the fractional-order derivative approaches 1 proved an excellent tool for solving and predicting the model.

Malaria remains a major public health burden in Nigeria, where climatic variability plays a critical role in shaping transmission dynamics. This study develops and evaluates climate-based predictive models for malaria incidence by integrating historical malaria surveillance data (2018–2023) with key meteorological variables, temperature, precipitation, humidity, and wind speed, across diverse ecological zones. Both traditional statistical and advanced machine learning (ML) approaches were employed to capture linear and nonlinear relationships between climate factors and malaria occurrence. Multiple Linear Regression (MLR) served as the baseline model, while Random Forest (RF), Support Vector Regression (SVR), Artificial Neural Network (ANN), Gradient Boosting Regression (GBR), XGBoost, and Long Short-Term Memory (LSTM) networks represented ML alternatives. Model performance was assessed using RMSE, MAE, R², and MAPE. Results revealed that ensemble-based ML models significantly outperformed MLR, with XGBoost emerging as the best performer (R² = 0.89; RMSE = 27.9; MAPE = 9.8%), followed closely by GBR and RF. The LSTM model effectively captured temporal dependencies (R² = 0.83), while MLR exhibited limited predictive ability (R² = 0.61). Regional analyses indicated that prediction accuracy was higher in areas with stable climatic conditions and reliable data reporting, whereas variability and data gaps in conflict-affected zones reduced performance. The findings highlight the superior predictive power and adaptability of ensemble ML methods for climate-driven malaria forecasting. The study offers an evidence-based framework for integrating these models into Nigeria’s early warning systems, supporting timely and geographically targeted malaria control interventions.

In this paper, we consider an approximate analytical method of optimal homotopy asymptotic method-least square (OHAM-LS) to obtain a solution of nonlinear fractional-order gradient-based dynamic system (FOGBDS) generated from nonlinear programming (NLP) optimization problems. The problem is formulated in a class of nonlinear fractional differential equations, (FDEs) and the solutions of the equations, modelled with a conformable fractional derivative (CFD) of the steepest descent approach, are considered to find the minimizing point of the problem. The formulation extends the integer solution of optimization problems to an arbitrary-order solution. We exhibit that OHAM-LS enables us to determine the convergence domain of the series solution obtained by initiating convergence-control parameter C-j ' s. Three illustrative examples were included to show the effectiveness and importance of the proposed techniques.

Solving fractional optimal control problems (FOCPs) with an approximate analytical method has been widely studied by many authors, but to guarantee the convergence of the series solution has been a challenge. We solved this by integrating the Galerkin method of optimization technique into the whole region of the governing equations for accurate optimal values of control-convergence parameters $C_j^s$ . The arbitrary-order derivative is in the conformable fractional derivative sense. We use Euler–Lagrange equation form of necessary optimality conditions for FOCPs, and the arising fractional differential equations (FDEs) are solved by optimal homotopy asymptotic method (OHAM). The OHAM technique speedily provides the convergent approximate analytical solution as the arbitrary order derivative approaches 1. The convergence of the method is discussed, and its effectiveness is verified by some illustrative test examples.