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 ...

In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory ...

Whether it's physical phenomena, share prices or climate models—many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

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 ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues. The trajectory of a storm ...

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...