During the culminating year of the twentieth century, the prolific and profound theory of wavelets was created, thanks to the collective and tireless efforts of physicists, mathematicians, and engineers. Since their inception, wavelets have gained respectable status due to their versatile applicability and have grown at an exponential rate in diverse fields of science and engineering including signal and image processing, sampling theory, approximation theory, geophysics, astrophysics, quantum mechanics, turbulence and fluid dynamics, statistics, finance and economics, biological and chemical sciences and many others. Besides these, parallel developments of wavelet theory have also been witnessed in quaternion and Clifford algebras, including the construction and characterization of quaternion-valued wavelets, octonion-valued wavelets and Clifford-valued wavelets of dimensionn=2,3(mod 4) and general order n. On the other hand, wavelet-based numerical methods (wavelet-Galerkin methods, wavelet collocation methods, wavelet optimized numerical methods, and Lagrange particle wavelet methods) have attained a significant place in numerical analysis mainly due to their simple procedure, easy computation and rapid convergence. As of now, these methods have overruled the existing approximation methods due to their outstanding performance, especially for solving different problems arising in the theory of differential and integral equations.

The theory of wavelets is being continuously refined to tackle different problems arising in various branches of science and engineering. As a consequence, some offshoots of the classical wavelet transform came into existence, such as Stockwell transforms, linear canonical wavelet transforms, and many more. To address the directional insensitivity of the classical wavelets, the notions of ridgelets, curvelets, contourlets, riplets, shearlets, surfacelets, flaglets, beamlets,bendlets and Taylorlets were introduced in the recent literature (X-lets). Nevertheless, many important areas pertaining to the development of these geometrical wavelets have yet to be explored.

The main purpose of this special issue is to provide a multidisciplinary forum of discussion among scientists who have been interested in investigating and studying diverse areas related to wavelets, frames and their applications. This Special Issue welcomes articles which are closely related to wavelets and their applications in physical, chemical, biological and engineering sciences. Original research, as well as review articles, are welcome.

Potential topics include but are not limited to the following:

• Wavelet transforms and their generalizations
• Wavelet transforms on quaternion and Clifford algebras
• Wavelet frames and their generalizations
• Wavelet based numerical methods
• Application of wavelets in physical, chemical, biological, and engineering sciences