In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

A system of U(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz. The highest weight property of the solutions is proved and some examples of solutions are calculated explicitly.

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.

In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= beta x_n(1- x_n), n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Huku...

We define an extended fuzzy equivalence relation, discuss some basic properties of extended fuzzy equivalence relations, find the extended fuzzy equivalence relation generated by a fuzzy relation in a set, and give some lattice theoretic properties of extended fuzzy equivalence relations.

In this paper, we define the notion of (dual) multi-fuzzy normedspaces and describe some properties of them. We then investigate Ulam-Hyers stability of Jensen's functional equation for mappings from linear spaces into  multi-fuzzy normed spaces. We establish an asymptotic behavior of the Jensen equation in the framework of multi-fuzzy normed spaces.

The second order linear difference equation (1) ∆(rk∆xk) + ckxk+1 = 0, where rk 6= 0 and k ∈ , is considered as a special type of symplectic systems. The concept of the phase for symplectic systems is introduced as the discrete analogy of the Bor̊uvka concept of the phase for second order linear differential equations. Oscillation and nonoscillation of (1) and of symplectic systems are investiga...

We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium x\over \tilda=1. As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not event...