In recent years, various families of special functions such as those named after Gamma, Beta, and hypergeometric functions have been found to be remarkably important, due mainly to their demonstrated applications in numerous diverse and widespread areas of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these special functions are used as useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations, fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions in mathematical physics and applied mathematics.

This Special Issue aims to provide a forum for researchers and scientists to communicate their recent developments and to present recent results in theory and applications of partial differential equations. Original research papers and review articles focused on the fields of the construction and investigation of solutions to both well-posed and ill-posed boundary value problems for partial differential equations - as well as their related applications-are welcomed.

Potential topics include but are not limited to the following:

• Fractional-order ordinary differential equation (ODEs) and partial differential equations (PDEs) involving special functions and their applications
• Fractional-order integrals and fractional-order derivatives associated with special functions of mathematical physics and applied mathematics
• Problems involving positive operators associated with special functions with classical and nonclassical boundary conditions
• New methods in theory and applications of PDEs
• Stochastic PDE models and applications
• Computational methods in PDEs