# Volume 7 (2015), Number 2

## On Subclass of Harmonic Univalent Functions Deﬁned by Generalized Salagean Operator and Ruscheweyh Operator

### Author(s): MOHAMMAD AL-KASEASBEH and MASLINA DARUS

**Abstract:** A subclass of complex-valued harmonic univalent function deﬁned by generalized Salagean operator and
Ruscheweyh operator is introduced. Coefficient bounds, distortion theorem, and other properties of this class are obtained.

## A Mathematical Model to Extend the Theory of Relativity when the Velocities of the Mass are Larger than the Velocity of the Light c and its Possible Application in Cosmology

### Author(s): MALVINA BAICA and MIRCEA CARDU

**Abstract:** In this paper we analyze the subject in the title accepting that the Mathematical model from the Theory of
Relativity (RT) corresponding to the velocity $v<c$ is also valid to the case $v>c$. In the same time we apply the method
to solve the equations of type ${y}^{2}\pm \phi =0$
in their simplest form ${y}^{2}\pm 1=0$ developed in
[9] and [10]. Here we assign the “dual” solutions for $v<c$ and $v>c$ respectively and the “bipolar” solutions for the two forms of
the Mass in the Universe called Matter (MA) and Antimatter (AM), respectively.

## Global Existence of Solution for Reaction Diﬀusion Systems with a Full Matrix

### Author(s): K. BOUKERRIOUA

**Abstract:** The aim of this paper is to study the global existence in time of solutions for some class of reaction-diffusion
systems with full matrix.Our techniques are based on invariant regions and Lyapunov functional methods.Our goal is to show, under
suitable assumptions, that the proposed model have a global solution for a large class of the functions $f$ and $g$.

## An Integral Equation from Physics - A Synthesis Survey - Part II

### Author(s): MARIA DOBRIȚOIU

**Abstract:** This part of the synthesis survey on the study of the integral equation from physics:

$$x\left(t\right)={\int}_{a}^{b}K\left(t,s,x\left(s\right),x\left(a\right),x\left(b\right)\right)ds+f\left(t\right),\phantom{\rule{1em}{0ex}}t\in \left[a,b\right].$$ |

## Approximate Solution of a Nonlinear Fractional Ordinary Differential Equation by DGJ Method

### Author(s): YIYING FENG and YUE HU

**Abstract:** Applying the new iterative method (DGJM), which have been used to handle the nonlinear models, we investigate the
approximate analytical solutions for a nonlinear fractional ordinary differential equation (FODE), where the fractional derivatives are
considered in Caputo sense. On the process of dealing with nonlinear terms, we particularly employ Taylor series expansion to obtain
the analytical solutions.

## The generalized $\left(s,t\right)$-Fibonacci and Fibonacci matrix sequences

### Author(s): AHMET İPEK, KAMIL ARI and RAMAZAN TÜRKMEN

**Abstract:** In this paper, we study the generalizations of the $\left(s,t\right)$-Fibonacci and
Lucas sequences and the $\left(s,t\right)$-Fibonacci and Lucas matrix sequences. We present relationship
between the $\left(s,t\right)$-Fibonacci matrix and generalized Fibonacci matrix sequences. Binet’s
formula for the generalized $\left(s,t\right)$-Fibonacci matrix sequence is derived. We establish several
identites for the generalized $\left(s,t\right)$-Fibonacci and Fibonacci matrix sequence. We give some partial
sum formulas for the generalized $\left(s,t\right)$-Fibonacci and Fibonacci matrix sequence. Also, we ﬁnd out
relationship between the $\left(s,t\right)$-Fibonacci matrix sequence and the famous Bernoulli numbers.

## On the determination of the eigenvalues for Airy fractional diﬀerential equation with turning point

### Author(s): A. NEAMATY, B. AGHELI and R. DARZI

**Abstract:** The present paper reports the result of a study on eigenvalue approximation of the Airy fractional differential equation,
using a new deﬁnition of fractional derivative called conformable fractional derivative. We have tried to present the approximate solution of
the eigenvalue of Airy fractional differential equation (AFDE) on the right half-line and the left half-line with a turning point through
applying the Adomian decomposition method. All numerical calculations in this manuscript were performed on a PC applying some programs written
in Mathematica.