Difference Equations and Z - Transforms

Numerical Solution of Volterra-Fredholm Integral Equations with The Help of Inverse and Direct Discrete Fuzzy Transforms and Collocation Technique

Solving a Class of Partial Differential Equations by Differential Transforms Method

‎In this work, we find the differential transforms of the functions $tan$ and‎ ‎$sec$‎, ‎and then we applied this transform on a class of partial differential equations involving $tan$ and‎ ‎$sec$‎.

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...

On meromorphic solutions of certain type of difference equations

‎We mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+P(z)f(z+c)^n=Q(z)$‎, ‎which is a supplement of previous‎ ‎results in [K‎. ‎Liu‎, ‎L. Z‎. ‎Yang and X‎. ‎L‎. ‎Liu‎, ‎Existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎Czechoslovak Math. J. 61 (2011)‎, no. 2, ‎565--576‎, and X‎. ‎G‎. ‎Qi‎...

Some results on value distribution of the difference operator

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...