Arabian Journal of Mathematics最新文献

In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry analysis as part of our approach together with some number theoretic functions. Our findings generalize certain results in the literature.

In this paper, we study the heat transfer modeling during freezing of a biological tissue and present an analytical approach for solving the heat transfer problem in cryosurgery. We consider a time-fractional bio-heat equation in the cylindrical coordinate and employ the Wiener–Hopf technique to find the temperature of tissue in two different domains by the factorization of associated Wiener–Hopf kernel. We discuss the fundamental roles of the Bessel and Wright functions in determining the analytical solution of fractional cryosurgery problem.

In this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo fractional derivatives with initial and integral conditions. Some new results on the existence and uniqueness of a solution for the model are obtained as well as the Ulam stability of the solutions. Two examples are provided to show the applicability of our results.

We study the weak convergence of infinite products of convex combinations of operators in complete CAT(0) spaces. We provide a new approach to this problem by considering a constructive selection of convex combinations in CAT(0) spaces that does not depend on the order of the involved elements and retain continuity properties with respect to them.

The classical symmetry method is often employed to find precise solutions to differential equations. This method has yielded several new symmetry reductions and exact solutions for numerous theoretically and physically relevant partial differential equations. These results, as well as the symmetries of a variety of specific cases of the Fokker–Planck equation, were presented in this study using the classical Lie symmetry approach. New exact solutions to the Fokker–Planck equations are provided for each of the six cases.

We establish a relationship between asymptotic regularity and common stationary points of multivalued mappings on a metric space. As a consequence of our results, we obtain a new common fixed point result for two asymptotically regular single-valued mappings. Our work significantly improves and complements comparable results in the literature.

This paper presents several properties and relations that satisfy the components of a bicomplex holomorphic function. It also exhibits several analogies and differences with the case of analytic functions.

In this paper, we consider a coupled system of hyperbolic and biharmonic-wave equations with variable exponents in the damping and coupling terms. In each equation, the damping term is modulated by a time-dependent coefficient a(t) (or b(t)). First, we state and prove a well-posedness theorem of global weak solutions, by exploiting Galerkin’s method and some compactness arguments. Then, using the multiplier method, we establish the decay rates of the solution energy, under suitable assumptions on the time-dependent coefficients and the range of the variable exponents. We end our work with some illustrative examples.

In this paper, we consider a weighted fractional stochastic integro-differential equation with infinite delay and nonzero initial values involving a Riemann–Liouville fractional derivative of order (1/2<alpha <1). The existence of a mild solution is investigated using fractional calculus, stochastic analysis, and the fixed point theorem. An example is also provided to illustrate the obtained result.

Given a Musielak–Orlicz function (varphi (x,s):Omega times [0,infty )rightarrow {mathbb R}) on a bounded regular domain (Omega subset {mathbb R}^n) and a continuous function (M:[0,infty )rightarrow (0,infty )), we show that the eigenvalue problem for the elliptic Kirchhoff’s equation (-Mleft( int limits _{Omega }varphi (x,|nabla u(x)|)textrm{d}xright) text {div}left( frac{partial varphi }{partial s}(x,|nabla u(x)|)frac{nabla u(x)}{|nabla u(x)|}right) =lambda frac{partial varphi }{partial s}(x,|u(x)|)frac{u(x)}{|u(x)|} ) has infinitely many solutions in the Sobolev space (W_0^{1,varphi }(Omega )). No conditions on (varphi ) are required beyond those that guarantee the compactness of the Sobolev embedding theorem.