Open Journal of Mathematical Sciences (OMS)

Locally harmonious coloring is a relax version of standard harmonious coloring which only needs that the color pairs for adjacent edges are different. In this remark, we introduce the concept of fractional locally harmonious coloring, and present some basic facts for this coloring.

In the present article, a time fractional diffusion problem is formulated with special boundary conditions, specifically the nonlocal boundary conditions. This new problem is then solved by utilizing the Laplace transform method coupled to the well-known Adomian decomposition method after employing the modified version of Beilin’s lemma featuring fractional derivative in time. The Caputo fractional derivative is used. Some test problems are included.

In this paper, we introduce and study the classes \(S_{n,\mu}(\gamma,\alpha,\beta,\) \(\lambda,\nu,\varrho,\mho)\) and \(R_{n,\mu}(\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho)\) of functions \(f\in A(n)\) with \((\mu)z(D^{\mho+2}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z))^{‘} \) \(+(1-\mu)z(D^{\mho+1}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z))^{‘}\neq0\), where \(\nu>0,\varrho,\omega,\lambda,\alpha,\mu \geq0, \mho\in N_{0}, z\in U\) and \(D^{\mho}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z):A(n)\longrightarrow A(n),\) is the linear differential operator, newly defined as
\( D^{\mho}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z)=z-\sum_{k=n}^{\infty}\left( \dfrac{\nu+k(\varrho+\lambda)\omega^{\alpha}}{\nu} \right)^{\mho} a_{k+1}z^{k+1}. \)
Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion relation for the functions included in the classes \(S_{n,\mu} (\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) and \(R_{n,\mu}(\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) are given.

This article presents, effects of fractional order derivative and magnetic field on double convection flow of viscous fluid over a moving vertical plate with constant temperature and general concentration. The model is fractionalized by using Caputo-Fabrizio derivative operator. Closed form solutions of the fluid velocity, concentration and temperature are obtained by means of the Laplace transform. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo-Fabrizio time-fractional parameter , magnetic parameter , Prandtl and Grashof numbers on velocity field.

We shall present new oscillation criteria of second order nonlinear difference equations with a non-positive neutral term of the form \(\Delta(a(t)(\Delta(x(t)-p(t)x(t-k)))^{\gamma})+q(t)x^{\beta}(t+1-m)=0,\) with positive coefficients. Examples are given to illustrate the main results.

In this work we develop the weighted square integral estimates for the second derivatives of weak subsolution of forth order Laplace equation. It is natural generalization of inequalities develop for the Superharmonic functions in [1].

With the extensive application of ontology in the fields of information retrieval and artificial intelligence, the ontology-based conceptual similarity calculation becomes a hot topic in ontology research. The essence of ontology learning is to obtain the ontology function through the learning of ontology samples, so as to map the vertices in each ontology graph into real numbers, and finally determine the similarity between corresponding concepts by the difference between real numbers. The essence of ontology mapping is to calculate concepts from different ontologies. In this paper, we introduce new ontology similarity computing in view of stochastic primal dual coordinate method, and two experiments show the effectiveness of our proposed ontology algorithm.

In this paper, dynamics of a two-dimensional Fitzhugh-Nagumo model is discussed. The discrete-time model is obtained with the implementation of forward Euler’s scheme. We present the parametric conditions for local asymptotic stability of steady-states. It is shown that the two-dimensional discrete-time model undergoes period-doubling bifurcation and Neimark-Sacker bifurcation at its positive steady-state. Furthermore, in order to illustrate theoretical discussion some interesting numerical examples are presented.

Let \(D\) be a connected digraph of order \(n\); \((n \geq 3)\) and let \(B(D)=\{B_1,B_2,\ldots,B_N\}\) be a set of blocks of \(D\). The block digraph \(Q=\mathbb{B}(D)\) has vertex set \(V(Q)=B(D)\) and arc set \(A(Q)=B_iB_j\) and \(B_i,B_j \in V(Q),\) \(B_i,B_j\) have a cut-vertex of \(D\) in common and every vertex of \(B_j\) is reachable from every other vertex of \(B_i\) We study the properties of \(\mathbb{B}(D)\) and present the characterization of digraphs whose \(\mathbb{B}(D)\) are planar; outerplanar; maximal outerplanar; minimally nonouterplanar; Eulerian; and Hamiltonian.

In this paper, the notions of fuzzy zero-divisors and fuzzy integral domains are illustrated. Some fundamental properties of fuzzy integral domains are proved. Moreover, the notions of fuzzy regular element and fuzzy regular sequences are defined. It is shown that any permutation (resp. any positive integral power) of a fuzzy regular sequence is again a fuzzy regular sequence. At the end, fuzzy regular sequences of two fuzzy submodules are related with the help of fuzzy short exact sequences.