Linear differential equations with fast growing coefficients in the unit disc
OMA-Vol. 4 (2020), Issue 1, pp. 38 – 48 Open Access Full-Text PDF
Benharrat Belaïdi, Mohamed Amine Zemirni
Abstract: In this article, we give new conditions on the fast growing analytic coefficients of linear complex differential equations to estimate the iterated \(p\)-order and iterated \(p\)-type of all solutions in the unit disc \(\mathbb{D}\), where \(p\in \mathbb{N}\backslash \{1\}\).
New fractional Hadamard and Fejér-Hadamard inequalities associated with exponentially \((h,m)\)-convex functions
EASL-Vol. 3 (2020), Issue 2, pp. 9 – 18 Open Access Full-Text PDF
Sajid Mehmood, Ghulam Farid,, Khuram Ali Khan, Muhammad Yussouf
Abstract: The aim of this paper is to establish some new fractional Hadamard and Fejér-Hadamard inequalities for exponentially \((h,m)\)-convex functions. These inequalities are produced by using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold for various kinds of convexities and well known fractional integral operators.
Leap Zagreb and leap hyper-Zagreb indices of Jahangir and Jahangir derived graphs
EASL-Vol. 3 (2020), Issue 2, pp. 1 – 8 Open Access Full-Text PDF
Fatima Asif, Zohaib Zahid, Sohail Zafar
Abstract: Topological indices are numerical parameters of a graph which characterize its topology. The second degree of a vertex in a graph is equal to the number of its second neighbors. In this paper, we will compute leap Zagreb indices and leap hyper-Zagreb indices of Jahangir graph and its line graph based on the 2-distance degree of the vertices. Moreover we will compute the same indices for the subdivision graph and the line graph of the subdivision of Jahangir graph.
A mathematical model of smoking behaviour in Indonesia with density-dependent death rate
OMS-Vol. 4 (2020), Issue 1, pp. 118 – 125 Open Access Full-Text PDF
Clara Mia Devira Simarmata, Nanang Susyanto, Iqbal J. Hammadi, Choirul Rahmaditya
Abstract: This work presents a mathematical model that investigates the impact of smokers on the transmission dynamics of smoking behavior in the Indonesian population. The population is classified into three classes: potential smokers, smokers, and ex-smokers. This model is described by non-linear differential equations using fractional quantities instead of actual populations by scaling the population of each class by the total population. There is also the density-dependent and density-independent death rate in the model to accommodate the difference between the death rate of potential smokers, smokers, and ex-smokers. In this model, two equilibrium points are found. One of them is the smoking-free equilibrium and the other relates to the presence of smoking. Then, the local stability of both equilibrium points is examined. Lastly, numerical simulations are carried out to illustrate the sensitivity of the smoker class to the parameters: the rate of non-smokers become smokers, the rate of smokers become smokers, also the rate of ex-smokers re-adapt smoking habit. The result of this paper can be considered to make a policy to reduce the number of smokers in Indonesia.
A few comments and some new results on JU-algebras
OMS-Vol. 4 (2020), Issue 1, pp. 110 – 117 Open Access Full-Text PDF
Daniel A. Romano
Abstract: In this article, we revisit the axioms of JU-algebras previously recognizable as ‘pseudo KU-algebras’, which we may call as ‘weak KU-algebras’ and discussed the definitions of some of their substructures. We also associate this class of algebras with the classes of BE-algebras and UP-algebras. In addition, we introduce and analyze some new classes of ideals in this class of algebras.
Higer-order commutators of parametrized Marcinkewicz integrals on Herz spaces with variable exponent
EASL-Vol. 3 (2020), Issue 1, pp. 56 – 70 Open Access Full-Text PDF
Omer Abdalrhman, Afif Abdalmonem, Shuangping Tao
Abstract: Let \(0<\rho<n\) and \(\mu_{\Omega}^{\rho}\) be the Parametrized Marcinkiewicz integrals operator. In this work, the bondedness of \(\mu_{\Omega}^{\rho}\) is discussed on Herz spaces \(\dot{K}_{p(\cdot)}^{\alpha,q(\cdot)}(\mathbb{R}^{n})\), where the two main indices are variable exponent. The boundedness of the commutators generated by BOM function, Lipschitz function and parametrized Marcinkiewicz integrals operator is also discussed.
