TY - JOUR
TI - Beyond Laplace and Fourier transforms: Challenges and future prospects
AU - He Ji-Huan
AU - Anjumd Naveed
AU - Hee Chun-Hui
AU - Alsolamif Abdulrahman Ali
JN - Thermal Science
PY - 2023
VL - 27
IS - 6
SP - 5075
EP - 5089
PT - Article
AB - Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations. Here we introduce a generalized integral transform, which is a generalization of the Fourier transform, Laplace transform, and other transforms, e.g., Sumudu transform, Aboodh transform, Pourreza transform, and Mohand transform, making the new transform much attractive and promising. Its basic properties are elucidated, and its applications to initial value problems and integral equations are illustrated, when coupled with the homotopy perturbation, it can be used for various non-linear problems, opening a new window for non-linear science.