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Latest Published Articles
ODAM-Vol. 3 (2020), Issue 1, pp. 1 – 7 Open Access Full-Text PDF
Prashant V. Patil, Girish G. Yattinahalli
Abstract: In this paper, we obtained some new properties of Zagreb indices. We mainly give explicit formulas to the second Zagreb index of semitotal-line graph (or middle graph), semitotal-point graph and total transformation graphs \(G^{xyz}.\)
A unified integral operator and further its consequences
OMA-Vol. 4 (2020), Issue 1, pp. 1 – 7 Open Access Full-Text PDF
Ghulam Farid
Abstract: The aim of this paper is to construct left sided and right sided integral operators in a unified form. These integral operators produce various well known integral operators in the theory of fractional calculus. Formulated integral operators of this study include generalized fractional integral operators of Riemann-Liouville type and operators containing Mittag-Leffler functions in their kernels. Also boundedness of all these fractional integral operators is derived from the boundedness of unified integral operators. The existence of new integral operators may have useful consequences in applied sciences besides in fractional calculus.
Positive solutions for boundary value problem of sixth-order elastic beam equation
OMS-Vol. 4 (2020), Issue 1, pp. 9 – 17 Open Access Full-Text PDF
Zouaoui Bekri, Slimane Benaicha
Abstract: In this paper, we study the existence of positive solutions for boundary value problem of sixth-order elastic beam equation of the form \(-u^{(6)}(t)=q(t)f(t,u(t),u^{‘}(t),u^{”}(t),u^{”’}(t),u^{(4)}(t),u^{(5)}(t)),~~0<t<1,\) with conditions \(u(0)=u^{‘}(1)=u^{”}(0)=u^{”’}(1)=u^{(4)}(0)=u^{(5)}(1)=0,\) where \(f\in C([0,1]\times[0,\infty)\times[0,\infty)\times(-\infty,0]\times(-\infty,0]\times[0,\infty)\times[0,\infty)\rightarrow [0,\infty))\). The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. We give sufficient conditions that allow us to obtain the existence of positive solution. The main tool used in the proof is the Leray-Schauder nonlinear alternative and Leray-Schauder fixed point theorem. As an application, we also give example to illustrate the results obtained.
A fixed point theorem for generalized weakly contractive mappings in \(b\)-metric spaces
OMS-Vol. 4 (2020), Issue 1, pp. 1 – 8 Open Access Full-Text PDF
Eliyas Zinab, Kidane Koyas, Aynalem Girma
Abstract: In this paper we establish a fixed point theorem for generalized weakly contractive mappings in the setting of \(b\)-metric spaces and prove the existence and uniqueness of a fixed point for a self-mappings satisfying the established theorem. Our result extends and generalizes the result of Cho [1]. Finally, we provided an example in the support of our main result.
Existence of solution for a nonlinear fifth-order three-point boundary value problem
OMA-Vol. 3 (2019), Issue 2, pp. 125 – 136 Open Access Full-Text PDF
Zouaoui Bekri, Slimane Benaicha
Abstract: In this paper, we explore the existence of nontrivial solution for the fifth-order three-point boundary value problem of the form \(u^{(5)}(t)+f(t,u(t))=0,\quad\text 0<t<1,\) with boundary conditions \(u(0)=0,\quad u^{‘}(0)=u^{”}(0)=u^{”’}(0)=0,\quad u(1)=\alpha u(\eta),\) where \(0<\eta<1\), \(\alpha\in\mathbb{R}\), \(\alpha\eta^{4}\neq1\), \(f\in C([0,1]\times\mathbb{R},\mathbb{R})\). Under certain growth conditions on the non-linearity \(f\) and using Leray-Schauder nonlinear alternative, we prove the existence of at least one solution of the posed problem. Furthermore, the obtained results are further illustrated by mean of some examples.
Visualization of polynomiography from new higher order iterative methods
OMA-Vol. 3 (2019), Issue 2, pp. 112 – 124 Open Access Full-Text PDF
Saba Freed, Amir Naseem, Muhammad Irfan Saleem
Abstract: Polynomiography is the art and science of visualization in approximation of zeros of polynomials. In this report, we visualize polynomiography of some complex polynomials via iterative methods presented in [1].