Description: Classical PDEs involve partial derivatives of a function of multiple variables describing physical quantities. These are crucial for understanding continuous processes across disciplines, with solutions often forming the basis for applied research and technological developments. Fractional PDEs are an extension of classical PDEs, which generalize derivatives to non-integer orders. These equations have become a valuable tool for modelling complex, real-world systems exhibiting features not adequately captured by traditional PDEs.

Spectral methods are known for their exceptional accuracy and efficiency in solving a wide range of differential equations with flexibility in handling various types of boundary conditions. These methods exhibit exponential convergence rates and are suitable for numerical simulations requiring precise solutions. These methods offer flexibility in choosing basis functions tailored to specific problem characteristics. Their ability to resolve high-frequency components and global nature makes them indispensable tools in scientific computing and engineering simulations, where precision and computational efficiency are paramount.

The class of methods and problems which cover the theme of the symposium are listed:

Class of Spectral Methods: Collocation Methods, Galerkin Methods, Tau Methods, Sparse Grid Methods, Pseudo Methods, Multidomain Methods, Finite Difference / Finite Volume Methods, Hermite and Laguerre Spectral Methods, Radial Basis Function Spectral Methods, Hybrid Spectral Methods and much more…

Class of Problems: Fluid Dynamics, Quantum Mechanics, Electromagnetics, Structural Mechanics, Meteorology, Climate Modeling, Parametrized PDEs, Time-dependent PDEs, Stochastic PDEs, Complex PDEs, Singular PDEs, Turbulence Modeling, Image Processing, Elasticity, Geophysics, Nonlinear Wave Equation Solitons, Pattern Formation, Travelling Waves, Mathematical Physics, Biological Models, Epidemiological Models, and much more fractional PDEs …

Publications: Extended abstracts will be published in Special Volume of the American Institute of Physics Conference Proceedings. For details, please refer to the link: Papers–ICNAAM 2025.

Also, the papers can be considered for a special issue of the journal Fractal and Fractional. For details, please refer to the link: Special Issue: Fractional Equations and Applications.