Bessel functions on time scales and applications to partial dynamic equations

Key Points

• The aim is to investigate Bessel functions on time scales and derive fundamental solutions for certain partial dynamic equations.
• Introduced Bessel functions and modified Bessel functions of integer order on time scales.
• Established basic properties of these functions.
• Derived formulas for fundamental solutions of the discrete diffusion equation with backward time differences.
• New formulations for fundamental solutions of partial dynamic equations were obtained.
• Innovative approaches for handling the discrete case were developed.
• The findings highlight unique relationships between Bessel functions and dynamic systems.