In recent years, there has been a growing interest in setting up a modeling and solving mathematical problems in order to explain numerous experimental findings which are relevant to industrial applications.

Distributions are also known as generalized functions which generalize the idea of classical functions and allow us to extend the concept of derivative to all continuous functions. The theory of distributions has applications in various fields especially in science and engineering where there are many noncontinuous phenomena that naturally lead to differential equations whose solutions are distributions, such as the delta distribution, and, therefore, distributions can help us to develop an operational calculus in order to investigate linear ordinary differential equations as well as partial differential equations with constant and variable coefficients through their fundamental solutions.

Considering some regular operations which are valid for ordinary functions such as addition, multiplication by scalars can be extended into distributions. Other operations can only be defined for certain restricted subclasses; these are called irregular operations. However, generalized functions are useful tools to extend the concept of derivative to all continuous functions and are further used to formulate generalized solutions of partial differential equations. They are important in physics and engineering where many noncontinuous problems naturally lead to differential equations whose solutions are distributions, such as the Dirac delta distribution.

This special issue will focus on the irregular operations with integrals transform, special functions, and their applications with fractional orders. A further relationship between linear and nonlinear partial differential equations and generalized functions is considered. Potential topics include, but are not limited to:

• Integral transforms and their extension to distributions
• Special functions and solutions to the fractional differential equations
• Radon transform and its applications in CT scan
• Financial modeling and role of generalized functions

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