مشخصات پژوهش

Nonlinear integral equations involving fractional operators play a crucial role in mathematical modeling of real-world problems across physics, engineering, biology, and finance. In particular, the Riemann–Liouville fractional operator has been widely used to capture hereditary and memory effects in systems where classical models fail to provide accurate descriptions. These equations arise naturally in fields such as viscoelasticity, anomalous diffusion, signal processing, and population dynamics. However, their analytical solutions are extremely limited due to the combined complexity of nonlinearity and the fractional nature of the operator.‎ The necessity of this research stems from the lack of exact solutions for most nonlinear fractional integral equations and the pressing demand for efficient numerical or semi-analytical methods. Standard numerical approaches, while useful, often suffer from high computational cost, difficulties in handling singularities, or lack of convergence guarantees. Thus, there is a need for more robust and mathematically elegant methods that can approximate solutions with high accuracy and computational efficiency.‎