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Growth of solutions of a class of linear fractional differential equations with polynomial coefficients

Hamouda Saada, Mahmoudi Sofiane

Opuscula Mathematica

2022

Vol. 42, no. 3

415--426

This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman–Valiron theorem in the fractional calculus.

Properties of entire solutions of some linear PDE's

Bandura A, Skaskiv O., Filevych P.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 2

17--28

In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1. Also, we found a positive continuous function l such that entire solutions of the homogeneous linear differential equation with arbitrary fast growth have a bounded l -index and estimated its growth.