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Latest Published Articles

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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Existence result for a singular semipositone dynamic system on time scales

OMS-Vol. 4 (2020), Issue 1, pp. 86 – 97 Open Access Full-Text PDF
Arzu Denk Oguz, Fatma Serap Topal
Abstract: We concentrate on investigating the existence of positive solutions for the system of second order singular semipositone m-point boundary value problems in this article. We emphasize that the nonlinear term may take a negative value and be singular. By the properties of Green’s function and applying fixed point theorem in cones, existence results for positive solutions are obtained. Also, we provide an example to make our results clear and easy for readers to understand the existence result.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC