A note on fractional Bessel equation and its asymptotics

作者：Okrasinski Wojciech^*; Plociniczak Aukasz

来源：Fractional Calculus and Applied Analysis, 2013, 16(3): 559-572.

DOI：10.2478/s13540-013-0036-5

• fractional calculus
• fractional ordinary differential equation
• Bessel function
• asymptotic analysis

In this note we propose a fractional generalization of the classical modified Bessel equation. Instead of the integer-order derivatives we use the Riemann-Liouville version. Next, we solve the fractional modified Bessel equation in terms of the power series and provide an asymptotic analysis of its solution for large arguments. We find a leading-order term of the asymptotic formula for the solution to the considered equation. This behavior is verified numerically and shows high accuracy and fast convergence. Our results reduce to the classical formulas when the order of the fractional derivative goes to integer values.

• 出版日期2013-9