Anti complex fuzzy subgroups under \(s\)-norms
EASL-Vol. 3 (2020), Issue 4, pp. 1 – 10 Open Access Full-Text PDF
Rasul Rasuli
Abstract: In this study, we define anti complex fuzzy subgroups and normal anti complex fuzzy subgroups under $s$-norms and investigate some of characteristics of them. Later we introduce and study the intersection and composition of them. Next, we define the concept normality between two anti complex fuzzy subgroups by using \(s\)-norms and obtain some properties of them. Finally, we define the image and the inverse image of them under group homomorphisms.
Complex dynamics of a fractional-order predator-prey interaction with harvesting
ODAM-Vol. 3 (2020), Issue 3, pp. 24 – 32 Open Access Full-Text PDF
Rizwan Ahmed
Abstract: Harvesting has a strong impact on the dynamic evolution of a population subjected to it. In this paper, a fractional-order predator-prey interaction is studied with harvesting affecting both predator and prey populations. Local stability of the coexistence equilibrium point is discussed depending upon the harvesting of prey. Moreover, period-doubling and Neimark-Sacker bifurcations are studied for a wide range of constant harvesting effort of prey.
A differential inequality and meromorphic starlike and convex functions
OMA-Vol. 4 (2020), Issue 2, pp. 93 – 99 Open Access Full-Text PDF
Kuldeep Kaur Shergill, Sukhwinder Singh Billing
Abstract: In the present paper, we study a differential inequality involving certain differential operator. As a special case of our main result, we obtained certain differential inequalities implying sufficient conditions for meromorphic starlike and meromorphic convex functions of certain order.
Coupled coincidence and coupled common fixed points of a pair for mappings satisfying a weakly contraction type T-coupling in the context of quasi \(\alpha\)b-metric space
OMS-Vol. 4 (2020), Issue 1, pp. 369 – 376 Open Access Full-Text PDF
Kidane Koyas, Solomon Gebregiorgis
Abstract: In this paper, we have established a theorem involving a pair of mappings satisfying a weakly contraction type condition in the context of quasi \(\alpha\)b-metric space and proved the existence and uniqueness of coupled coincidence and coupled common fixed points. The concept of weakly compatibility of the pair of maps is applied to show the uniqueness of coupled common fixed point. This work offers an extension to the published work of Nurwahyu and Aris [1].
Existence results for a class of nonlinear degenerate \((p,q)\)-biharmonic operators
OMS-Vol. 4 (2020), Issue 1, pp. 356 – 368 Open Access Full-Text PDF
Albo Carlos Cavalheiro
Abstract: In this paper we are interested in the existence of solutions for Navier problem associated with the degenerate nonlinear elliptic equations in the setting of the weighted Sobolev spaces.
Existence of solution a fractional differential equation
ODAM-Vol. 3 (2020), Issue 3, pp. 14 – 23 Open Access Full-Text PDF
Zouaoui Bekri, Slimane Benaicha
Abstract: In this paper, we study the existence of nontrivial solution for the fractional differential equation of order \(\alpha\) with three point boundary conditions having the following form
$$
D^{\alpha}u(t)=f(t,v(t),D^{\nu}v(t)),\quad t\in(0,T)$$
$$u(0)=0,\quad u(T)=au(\xi),$$
where \(1<\alpha<2\), \(\nu, a>0\), \(\xi\in (0,T)\), \(T^{\alpha-1}+a\xi^{\alpha-1}\neq0\). \(D\) is the standard Riemann-Liouville fractional derivative operator and \(f\in C([0,1]\times\mathbf{R}^{2},\mathbf{R})\). Applying the Leray-Schauder nonlinear alternative we prove the existence of at least one solution. As an application, we also given some examples to illustrate the results obtained.
$$
D^{\alpha}u(t)=f(t,v(t),D^{\nu}v(t)),\quad t\in(0,T)$$
$$u(0)=0,\quad u(T)=au(\xi),$$
where \(1<\alpha<2\), \(\nu, a>0\), \(\xi\in (0,T)\), \(T^{\alpha-1}+a\xi^{\alpha-1}\neq0\). \(D\) is the standard Riemann-Liouville fractional derivative operator and \(f\in C([0,1]\times\mathbf{R}^{2},\mathbf{R})\). Applying the Leray-Schauder nonlinear alternative we prove the existence of at least one solution. As an application, we also given some examples to illustrate the results obtained.
