Generalized fractional differential ring
OMS-Vol. 5 (2021), Issue 1, pp. 279 – 287 Open Access Full-Text PDF
Zeinab Toghani, Luis Gaggero-Sager
Abstract: There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there is an infinite number of possible definitions of fractional derivatives, all are correct as differential operators each of them must be properly defined its algebra. We introduce a generalized version of fractional derivative that extends the existing ones in the literature. To those extensions it is associated a differentiable operator and a differential ring and applications that shows the advantages of the generalization. We also review the different definitions of fractional derivatives and it is shown how the generalized version contains the previous ones as a particular cases.
Spectral conditions for the Bipancyclic Bipartite graphs
ODAM-Vol. 4 (2021), Issue 2, pp. 48 – 51 Open Access Full-Text PDF
Rao Li
Abstract:Let \(G = (X, Y; E)\) be a bipartite graph with two vertex partition subsets \(X\) and \(Y\). \(G\) is said to be balanced if \(|X| = |Y|\) and \(G\) is said to be bipancyclic if it contains cycles of every even length from \(4\) to \(|V(G)|\). In this note, we present spectral conditions for the bipancyclic bipartite graphs.
Repeated sums and binomial coefficients
ODAM-Vol. 4 (2021), Issue 2, pp. 30 – 47 Open Access Full-Text PDF
Roudy El Haddad
Abstract:Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial coefficient identities will be shown in order to prove this definition. Using this new definition, we simplify some particular sums such as the repeated Harmonic sum and the repeated Binomial-Harmonic sum. We derive formulae for simplifying general repeated sums as well as a variant containing binomial coefficients. Additionally, we study the \(m\)-th difference of a sequence and show how sequences whose \(m\)-th difference is constant can be related to binomial coefficients.
Some fixed point theorems for \(F\)-expansive mapping in generalized metric spaces
OMA-Vol. 5 (2021), Issue 2, pp. 17 – 30 Open Access Full-Text PDF
Mohamed Rossafi, Abdelkarim Kari
Abstract: In this paper, we present the notion of generalized \(F\)-expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings. The findings of this paper, generalize and improve many existing results in the literature.
The hyper order and fixed points of solutions of a class of linear differential equations
OMA-Vol. 5 (2021), Issue 2, pp. 1 – 16 Open Access Full-Text PDF
Nour el imane Khadidja CHERIET, Benharrat BELAÏDI
Abstract: In this paper, we precise the hyper order of solutions for a class of higher order linear differential equations and investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second order case. These results generalize those of Nan Li and Lianzhong Yang and of Chen and Shon.
Strongest relation, cosets and middle cosets of \(AQFSC(G)\)
EASL-Vol. 4 (2021), Issue 3, pp. 1 – 7 Open Access Full-Text PDF
R. Rasuli
Abstract: The aim of this paper is to introduce strongest relation, cosets and middle cosets of anti \(Q\)-fuzzy subgroups of \(G\) with respect to \(t\)-conorm \(C.\) We investigate equivalent characterizations of them and we construct a new group induced by them, and give the homomorphism theorem between them.
