Fractional differential equations have recently gained popularity due to their ability to simulate a wide range of complex processes in various fields, including engineering, physics, biology, and ...

The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...