The possible orders of growth of solutions to linear fractional differential equations with polynomial coefficients

Key Points

• The aim is to explore the growth orders of solutions for a class of linear fractional differential equations with polynomial coefficients.
• Applied Nevanlinna theory in the complex domain.
• Utilized the generalized Wiman-Valiron theorem in fractional calculus.
• Employed Caputo fractional derivatives.
• Included several illustrative examples to support findings.
• Identified specific orders of growth for solutions to the equations.
• Demonstrated application of theoretical frameworks to deduce growth behavior.
• Provided examples illustrating the results within the framework of fractional calculus.