Fractional Concept

Fractional calculus extends traditional calculus by allowing non-integer orders of differentiation and integration, leading to models capable of capturing complex systems with memory effects and long-range dependencies. Current research focuses on developing and applying fractional models in diverse areas, including solving fractional differential equations (using methods like physics-informed neural networks and novel architectures such as fractional Kolmogorov-Arnold networks), enhancing neural network performance (through fractional activation and loss functions), and addressing challenges like the curse of dimensionality in high-dimensional fractional partial differential equations. These advancements offer improved accuracy and efficiency in modeling various phenomena across science and engineering, from anomalous diffusion to complex dynamical systems.