Hamed H. Alsulami

A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm–Volterra type

Abstract In this paper, the numerical solution of periodic Fredholm–Volterra integro–differential equations of first-order is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the periodic condition of the problem is satisfied. The exact solution u x is represented in the form of series in the space W 2 2 . In the mean time, the n-term approximate solution u n x is obtained and is proved to converge to the exact solution u x . Furthermore, we present an iterative method for obtaining the solution in the space W 2 2 . Some examples are displayed to demonstrate the validity and applicability of the proposed method. The numerical result indicates that the proposed method is straightforward to implement, efficient, and accurate for solving linear and nonlinear equations.

Three-Dimensional Mixed Convection Flow of Viscoelastic Fluid with Thermal Radiation and Convective Conditions

The objective of present research is to examine the thermal radiation effect in three-dimensional mixed convection flow of viscoelastic fluid. The boundary layer analysis has been discussed for flow by an exponentially stretching surface with convective conditions. The resulting partial differential equations are reduced into a system of nonlinear ordinary differential equations using appropriate transformations. The series solutions are developed through a modern technique known as the homotopy analysis method. The convergent expressions of velocity components and temperature are derived. The solutions obtained are dependent on seven sundry parameters including the viscoelastic parameter, mixed convection parameter, ratio parameter, temperature exponent, Prandtl number, Biot number and radiation parameter. A systematic study is performed to analyze the impacts of these influential parameters on the velocity and temperature, the skin friction coefficients and the local Nusselt number. It is observed that mixed convection parameter in momentum and thermal boundary layers has opposite role. Thermal boundary layer is found to decrease when ratio parameter, Prandtl number and temperature exponent are increased. Local Nusselt number is increasing function of viscoelastic parameter and Biot number. Radiation parameter on the Nusselt number has opposite effects when compared with viscoelastic parameter.

LEAVITT PATH ALGEBRAS OF FINITE GELFAND–KIRILLOV DIMENSION

Groebner–Shirshov Basis and Gelfand–Kirillov dimension of the Leavitt path algebra are derived.

Discussion on “Multidimensional Coincidence Points” via Recent Publications

We show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem.

Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation

The operational matrix of fractional-order Legendre functions method are considered.The fractional order convection-diffusion problem is solved.The problem can be used extensively in science and engineering as in oil reservoir simulations.Problems which, an initially discontinuous profile is propagated by diffusion and convection. In this paper, the application of the operational matrix of fractional-order Legendre functions (FLFs) to solve the time-fractional convection-diffusion equation has been investigated. Fractional calculus has been applied to model the engineering and physical processes which are best described with other mathematical tools. The time variable of the time-fractional convection-diffusion equation and its space variable have been approximated by FLFs and shifted Legendre polynomials, respectively. The fractional derivatives together with product matrices of FLFs are employed to convert the solution of this problem to the solution of a system of algebraic equations.

Structure of Leavitt path algebras of polynomial growth

We determine the structure of Leavitt path algebras of polynomial growth and discuss their automorphisms and involutions.

A Proposal to the Study of Contractions in Quasi-Metric Spaces

We investigate the existence and uniqueness of a fixed point of an operator via simultaneous functions in the setting of complete quasi-metric spaces. Our results generalize and improve several recent results in literature.

Fixed Points of Modified -Contractive Mappings in Complete Metric-Like Spaces

We introduce the notion of modified -contractive mappings in the setting of complete metric-like spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature.

Fixed Points of Generalized -Suzuki Type Contraction in Complete -Metric Spaces

We introduce the notion of generalized -Suzuki type contraction in -metric spaces and investigate the existence of fixed points of such mappings. The presented results generalize and improve several results of the topics in the literature.

On a time fractional reaction diffusion equation

A reaction diffusion equation with a Caputo fractional derivative in time and with various boundary conditions is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions will be analyzed.