On a class of functional difference equations: explicit solutions, asymptotic behavior and applications

For nu is an element of [0,1] and a complex parameter sigma, Re sigma > 0, we discuss a linear inhomogeneous functional difference equation with variable coefficients on a complex plane z is an element of C:(a(1)sigma + a(2)sigma(nu))Y(z + beta, sigma) -Omega(z)Y(z, sigma) = F(z, sigma), beta is an element of R, beta not equal 0, where Omega(z) and F(z) are given complex functions, while a1 and a2 are given real non-negative numbers. Under suitable conditions on the given functions and parameters, we construct explicit solutions of the equation and describe their asymptotic behavior as |z| -> +infinity. Some applications to the theory of functional difference equations and to the theory of boundary value problems governed by subdiffusion in nonsmooth domains are then discussed.