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.
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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.
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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.
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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.
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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.
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New Hadamard and Fejér-Hadamard fractional inequalities for exponentially \(m\)-convex function

EASL-Vol. 3 (2020), Issue 1, pp. 45 – 55 Open Access Full-Text PDF
Sajid Mehmood, Ghulam Farid, Khuram Ali Khan, Muhammad Yussouf
Abstract: In this article, we present new fractional Hadamard and Fejér-Hadamard inequalities for generalized fractional integral operators containing Mittag-Leffler function via a monotone function. To establish these inequalities we will use exponentially \(m\)-convex functions. The presented results in particular contain a number of fractional Hadamard and Fejér-Hadamard inequalities for functions deducible from exponentially \(m\)-convex functions.
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Analysis and numeric of mixed approach for frictional contact problem in electro-elasticity

OMA-Vol. 4 (2020), Issue 1, pp. 20 – 37 Open Access Full-Text PDF
M. Bouallala, EL-H. Essoufi A. Zafrar
Abstract: This work handle a mathematical model describing the process of contact between a piezoelectric body and rigid foundation. The behavior of the material is modeled with a electro-elastic constitutive law. The contact is formulated by Signorini conditions and Coulomb friction. A new decoupled mixed variational formulation is stated. Existence and uniqueness of the solution are proved using elements of the saddle point theory and a fixed point technique. To show the efficiency of our approach, we present a decomposition iterative method and its convergence is proved and some numerical tests are presented.
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Differential operators and Narayana numbers

ODAM-Vol. 3 (2020), Issue 1, pp. 37 – 40 Open Access Full-Text PDF
Jie Xiong, Qi Fang
Abstract: In this paper, we establish a connection between differential operators and Narayana numbers of both kinds, as well as a kind of numbers related to central binomial coefficients studied by Sulanke (Electron. J. Combin. 7 (2000), R40).
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Evaluation of convergent series by using finite parts

OMS-Vol. 4 (2020), Issue 1, pp. 98 – 109 Open Access Full-Text PDF
Ricardo Estrada
Abstract: We present a method to find the sum of a convergent series based on the computation of Hadamard finite part limits of partial sums. We give several illustrations, the main being the formulas for convergent series of the type \(\sum_{n=2}^{\infty}\frac{\left( -1\right) ^{n}\zeta\left( n,a\right) b^{n+k}}{n+k},\) where \(\zeta\left( s,a\right)\) is Hurwitz zeta function, \(\left\vert b\right\vert \leq\left\vert a\right\vert ,\) \(b\neq-a,\) and \(k\in\mathbb{N}.\)
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