مشخصات پژوهش

Caputo fractional differential equations are widely used to model memory-dependent and anomalous dynamic systems in physics, engineering, control theory, and biological processes. Their non-local fractional derivatives pose significant challenges for analytical solutions, and conventional numerical methods often struggle with accuracy, stability, and computational efficiency, particularly when applied to bounded intervals or long-time simulations. This highlights the necessity for advanced numerical techniques that can efficiently handle the global nature of fractional derivatives while providing high precision. A wavelet-based numerical method offers a powerful solution by leveraging the localization, multiresolution properties, and high-order approximation capabilities of wavelets, enabling accurate and efficient computation even in the presence of boundary constraints. The importance of this research lies in establishing a robust and versatile computational framework that improves the numerical treatment of Caputo fractional differential equations, advancing both theoretical understanding and practical applications across diverse scientific and engineering fields.