q-Karamata functions and second order q-difference equations

On a Class of Functional Differential Equations Having Slowly Varying Solutions

Functional differential equations with deviating arguments are studied for the first time in the framework of Karamata regularly varying functions. A sharp condition is established for the existence of slowly varying solutions for a class of second order linear equations of the form x′′ = q(t)x(g(t)), both in the retarded and in the advanced case.

A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations

The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order. The q-fractional differential equation usually describe the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative  of Caputo type with order  and scale index . We es...

Growth of meromorphic solutions for complex difference‎ ‎equations of Malmquist type

‎In this paper‎, ‎we give some necessary conditions for a complex‎ ‎difference equation of Malmquist type‎ $$‎sum^n_{j=1}f(z+c_j)=frac{P(f(z))}{Q(f(z))}‎,$$ ‎where $n(in{mathbb{N}})geq{2}$‎, ‎and $P(f(z))$ and $Q(f(z))$ are‎ ‎relatively prime polynomials in $f(z)$ with small functions as‎ ‎coefficients‎, ‎admitting a meromorphic function of finite order‎. ‎Moreover‎, ‎the properties of finite o...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations

It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...