Existence Solutions of the Complex Linear Differential Equations in QK,ω(p, q) Spaces

Abstract

In this article, we study the existence of solutions of the complex linear differential equation of the form f (n) + An−1(z)f (n−1) + ... + A1(z)f + A0(z)f = 0, where the coefficients A0, A1, ..., An are analytic functions in the unit disc. To carry out the existence of these solutions, we obtain some conditions for the coefficients which grantee the existence of the solutions in QK,ω(p, q) spaces.

Solution of complex differential equations with variable coefficients by using reduced differential transform

“…In [7] approximate solutions of equations of the same type have been found by using Taylor polynomial approximation. In [9], The Existence of solutions of the same type equations with analytical coefficients was investigated. In [8,14] f ′′ (z) + A(z) f (z) = 0 (1.4) which A(z) analytic equation has been investigated.…”