Arabian Journal of Mathematics最新文献

Sierpiński graphs are frequently related to fractals, and fractals apply in several fields of science, i.e., in chemical graph theory, computer networking, biology, and physical sciences. Functions and polynomials are powerful tools in computer mathematics for predicting the features of networks. Topological descriptors, frequently graph constraints, are absolute values that characterize the topology of a computer network. In this essay, Firstly, we compute the M-polynomials for Sierpiński-type fractals. We derive some degree-dependent topological invariants after applying algebraic operations on these M-polynomials.

This paper aims to study the existence and stability results concerning a fractional partial differential equation with variable exponent source functions. The local existence result for (alpha in (0,1)) is established with the help of the (alpha )-resolvent kernel and the Schauder-fixed point theorem. The non-continuation theorem is proved by the fixed point technique and accordingly the global existence of solution is achieved. The uniqueness of the solution is obtained using the contraction principle and the stability results are discussed by means of Ulam-Hyers and generalized Ulam-Hyers-Rassias stability concepts via the Picard operator. Examples are provided to illustrate the results.

Fourth order extended Fisher Kolmogorov reaction diffusion equation has been solved numerically using a hybrid technique. The temporal direction has been discretized using Crank Nicolson technique. The space direction has been split into second order equation using twice continuously differentiable function. The space splitting results into a system of equations with linear heat equation and non linear reaction diffusion equation. Quintic Hermite interpolating polynomials have been implemented to discretize the space direction which gives a system of collocation equations to be solved numerically. The hybrid technique ensures the fourth order convergence in space and second order in time direction. Unconditional stability has been obtained by plotting the eigen values of the matrix of iterations. Travelling wave behaviour of dependent variable has been obtained and the computed numerical values are shown by surfaces and curves for analyzing the behaviour of the numerical solution in both space and time directions.

The aim of this paper is twofold: first, we obtain various curvature inequalities which involve the Ricci and scalar curvatures of horizontal and vertical distributions of anti-invariant Riemannian submersion defined from conformal Kenmotsu space form onto a Riemannian manifold. Second, we obtain the Chen–Ricci inequality for the said Riemannian submersion. The equality cases of all the inequalities are studied. Moreover, these curvature inequalities are studied under two different cases: the structure vector field (xi ) being vertical or horizontal.

We prove that any homogeneous local representation (varphi :B_n rightarrow GL_n(mathbb {C})) of type 1 or 2 of dimension (nge 6) is reducible. Then, we prove that any representation (varphi :B_n rightarrow GL_n(mathbb {C})) of type 3 is equivalent to a complex specialization of the standard representation (tau _n). Also, we study the irreducibility of all local linear representations of the braid group (B_3) of degree 3. We prove that any local representation of type 1 of (B_3) is reducible to a Burau type representation and that any local representation of type 2 of (B_3) is equivalent to a complex specialization of the standard representation. Moreover, we construct a representation of (B_3) of degree 6 using the tensor product of local representations of type 2. Let (u_i), (i=1,2), be non-zero complex numbers on the unit circle. We determine a necessary and sufficient condition that guarantees the irreducibility of the obtained representation.

In this study, the theory of curves is reconstructed with fractional calculus. The condition of a naturally parametrized curve is described, and the orthonormal conformable frame of the naturally parametrized curve at any point is defined. Conformable helix and conformable slant helix curves are defined with the help of conformable frame elements at any point of the conformable curve. The characterizations of these curves are obtained in parallel with the conformable analysis Finally, examples are given for a better understanding of the theories and their drawings are given with the help of Mathematics.

Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely (P^{*}(n), M(n), T^{*}(n), L(n), K(n), A(n)), and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo (2^acdot 5^ell ) for (P^{*}(n)), modulo (2^3) for M(n) and (T^*(n)), where (a=3, 4) and (ell ge 1). For instance, we prove that for (nge 0),

In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki:

We study the asymptotic behavior of trajectories of the continuous dynamical system(CDS) associated with the discrete viscosity approximation method for fixed point problem of nonexpansive mapping (DDS) which was introduced by Moudafi (J Math Anal Appl 241:46–55, 2000). We establish that the trajectories x(t) of the continuous dynamical system (CDS) has an asymptotic behavior similar to the behavior of the sequences ((x_{n})) generated by the discrete viscosity approximation (DDS)

In this work, we obtain fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in complete (CAT_p(0)) metric spaces for (pge 2). Our results extend and improve many results in the literature.