https://cmcma.sbu.ac.ir/ Computational Mathematics and Computer Modeling with Applications (CMCMA) en daily 1 Mon, 01 Sep 2025 00:00:00 +0330 Mon, 01 Sep 2025 00:00:00 +0330 https://cmcma.sbu.ac.ir/article_106143.html https://cmcma.sbu.ac.ir/article_106142.html This study develops a numerical framework for solving Caputo-type fractional integro-differential equations using a hybrid formulation that integrates Legendre polynomial operational matrices within the Least Squares Support Vector Regression (LSSVR) paradigm. The proposed method reformulates the governing equations by representing all differential, integral, and integral-kernel operators in matrix form, derived from the orthogonality and recurrence properties of Legendre bases. This leads to a fully vectorized constrained optimization problem, subsequently reduced to a symmetric linear system via Karush–Kuhn–Tucker conditions. The approach retains the spectral convergence characteristics of orthogonal polynomial methods while incorporating the regularization and flexibility of LSSVR. Numerical experiments on benchmark problems with known solutions demonstrate exponential accuracy and high numerical stability across varying polynomial degrees. This formulation accommodates both Fredholm and Volterra integral structures and directly incorporates Caputo initial conditions without reformulation. The method is compatible with higher-dimensional extensions and adaptable to various kernel approximations. https://cmcma.sbu.ac.ir/article_106279.html This paper introduces a novel integration of Müntz polynomials into the Least Squares Support Vector Regression framework for addressing fractional optimal control problems. By utilizing Müntz basis functions as the mapping mechanism to project the problem into a higher-dimensional space, the proposed method reformulates the optimization challenge and resolves it efficiently through Maple's optimization tools. The effectiveness of this technique is validated via numerical experiments on benchmark fractional optimal control cases. Outcomes reveal that the approach delivers high precision in solving these problems, surpassing existing techniques in terms of accuracy and efficiency. https://cmcma.sbu.ac.ir/article_106311.html The global emergence of the Coronavirus (Covid-19) has resulted in far-reaching implications, encompassing substantial loss of human lives and the revelation of vulnerabilities in health systems across the globe. In response to this crisis, we revisited a prior model and extended it by incorporating a vaccination control element. This novel addition involves introducing a control factor into the vaccinated class to examine the repercussions of frequent vaccine administration as a strategic measure to mitigate the spread of COVID-19. Of particular interest in our investigation is the exploration of the criteria for the existence of numerical solutions to the model, achieved through the application of the Homotopy Perturbation Method. Our preliminary findings demonstrate that the vaccine control factor exerts substantial effects on both the susceptible and recovery classes within the model. This research contributes to the understanding of the dynamics of COVID-19 transmission, providing insights that can inform public health strategies in the ongoing global battle against the pandemic. https://cmcma.sbu.ac.ir/article_106412.html This study investigates the time–fractional Benjamin–Bona–Mahony (BBM) equation and the time–space fractional Benjamin–Bona–Mahony–Burgers (BBMB) equation, which model nonlinear wave propagation and dispersive transport phenomena in complex media exhibiting memory and nonlocal effects. To obtain efficient analytical approximations, the Shehu Transform Adomian Decomposition Method (STADM), a novel hybrid framework that combines the Shehu Transform (ST) with the Adomian Decomposition Method (ADM), is employed to derive series-form analytical solutions for both models. A four-term series approximation is obtained for each equation, and its convergence is verified through direct comparison with the corresponding exact analytical solution. The results exhibit excellent agreement, particularly as the fractional order approaches unity ($\alpha \to 1$), confirming the reliability and high accuracy of the proposed method. The influence of time and space fractional orders on the dynamic behavior of the solutions is analyzed through comprehensive 3D plots, which illustrate the effect of fractional parameters on wave dispersion and propagation. The main contributions of this work are: (i) the first systematic application of the STADM framework to the time–space fractional BBM and BBMB equations; (ii) the derivation of rapidly convergent analytical series solutions validated against exact results; and (iii) the demonstration of how fractional parameters modulate physical wave and diffusion processes. The proposed approach provides a simple, accurate, and computationally efficient tool for solving nonlinear fractional models relevant to wave evolution, pollutant dispersion, and oil-spill diffusion in coastal and environmental systems.