The natural transform (nt), a novel global method for solving fractional high-order differential equations (FDEs), is presented in this work. This technique functions as an all-encompassing integral ...

Fractional-order derivatives (FODs) have attracted considerable attention due to their intrinsic nonlocal nature, which enables them to capture memory and hereditary effects more accurately than ...

1 Tianjin Engineering Research Center of Civil Aviation Energy Environment and Green Development, Civil Aviation University of China, Tianjin, China. 2 Groupe d’Acoustigue de l’ Université de ...

Real-world problems in computational science and engineering that lack closed-form solutions often require the use of expensive numerical solvers. However, recent advances in scientific machine ...

The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both ...

Physics-informed convolutional recurrent network (PhyCRNet) can solve partial differential equations without labeled data by encoding physics constraints into the loss function. However, the ...

The study of reaction–diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of ...