Fractional Differential Equations Involving the Spherical Bessel Function j0: Analytical Solutions Via Laplace Transform | Chapter 03 | Physical Science: New Insights and Developments Vol. 4

 

This work addresses the resolution of fractional differential equations whose nonhomogeneous part is given by the spherical Bessel function 𝐽₀(𝑥). By using the fractional derivative in the sense of Caputo and the Laplace transform, a general analytical solution is obtained in terms of the generalised hypergeometric functions 2^𝐹3, revealing a recurrent structure in the solutions. Furthermore, particular cases for integer and fractional orders are presented, highlighting the appearance of special functions such as the sine integral and Fresnel functions. The results confirm the close relationship between fractional calculus and Bessel functions, proposing new perspectives for applications in mathematical physics.

 

Author(s) Details :-

 

Jorge Olivares Funes
Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile.

 

Pablo Martin
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.

 

Elvis Valero Kari
Universidad Mayor de San Andres, Bolivia.

 

Maria Teresa Veliz Aviles
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.

 

Please see the book here :- https://doi.org/10.9734/bpi/psniad/v4/6785