Journals – Page 71

Nonlocal initial value problems for Katugampola-Caputo type fractional differential equations on time scales

OMS-Vol. 3 (2019), Issue 1, pp. 07–10 Open Access Full-Text PDF

Alagarsamy Nandhini, Devaraj Vivek, Elsayed M. Elsayed

Abstract:In this paper, we study Katugampola fractional differential equations (FDEs) with nonlocal conditions on time scales. By means of standard fixed point theorems, some new sufficient conditions for the existence of solutions are established.

Weaker form of totally continuous functions

OMS-Vol. 3 (2019), Issue 1, pp. 01–06 Open Access Full-Text PDF

Md. Hanif Page and Lakshmi Narayan Mishra

Abstract:The objective of this paper is to study new type of continuous functions called totally $\alpha$gs-continuous functions using $\alpha$gs-open sets. Furthermore we discuss covering properties and obtain their characterizations by including counter examples.

Higher order nonlinear equation solvers and their dynamical behavior

OMA-Vol. 2 (2018), Issue 2, pp. 172–193 | Open Access Full-Text PDF

Sabir Yasin, Amir Naseem

Abstract:In this report we present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. To check the validity and efficiency we compare of methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method by solving some test examples. Numerical results shows that our developed methods are more effective. Finally, we compare polynomigraphs of our developed methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method.

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Silicon Carbide $Si_{2}C_{3}I[r,s]$ and $Si_{2}C_{3}II[r,s]$

EASL-Vol. 1 (2018), Issue 2, pp. 37–50 | Open Access Full-Text PDF

Abaid ur Rehman Virk, Mirza Naveed Jhangeer, M. A. Rehman

Abstract:Topological indices collect information from the graph of molecule and help to predict properties of underlined molecule. Zagreb indices are among the most studied topological indices due to its applications in chemistry. In this report we compute first and second reversed Zagreb indices and first and second reversed Hyper Zagreb indices for $Si_{2}C_{3}I[r,s]$ and $Si_{2}C_{3}II[r,s]$. Moreover we also compute first and second reversed Zagreb polynomials and first and second reversed Hyper Zagreb polynomials for $Si_{2}C_{3}I[r,s]$ and (Si_{2}C_{3}II[r,s]\).

Isolation, Purification and Complex Formation of Nicotine Alkaloid

EASL-Vol. 1 (2018), Issue 2, pp. 30–36 | Open Access Full-Text PDF

Sajid Mahmood, Saiqa Jameel, Zaheer Ahmad

Abstract:Nicotiana tabacum is rich with medicinal importance. The aim of the study is to isolate, purify and compare nicotine (3-[1-Methylpyrolidine-2 yl] pyridine) from different brands of cigarettes. Isolation is carried out by liquid-liquid extraction using ether as solvent. Crude nicotine samples are further purified with SPE (solid phase extraction) method. Nicotine crystals are complexed with zinc chloride ($ZnCl_{2}$). Fine and pure crystals of metal complexes are obtained with Nic-C and Nic-D. However, no complex formation is synthesized with Nic A and Nic-B due to impurities in the sample which is confirmed by thin layer chromatography. Antibacterial activity of the samples is carried out against different strains of bacteria which showed positive results for Nic-C and Nic-D. The outcomes of the study reveal that Zinc-Nicotine complexes can be used as therapeutic agents and anti-sickness agents in sickle cell disease.

Biological Synthesis and Characterization of Chromium (iii) Oxide Nanoparticles

EASL-Vol. 1 (2018), Issue 2, pp. 23–29 | Open Access Full-Text PDF

Zaheer Ahmad, Aisha Shamim, Sajid Mahmood, Tariq Mahmood, Farman Ullah Khan

Abstract:Nanoparticles are nanosized clusters with dimensions less than 100nm. Nanoparticles are fabricated by physical, chemical, and biological methods. Physical and chemical methods are energy intensive and involve hazards of contaminations. Biological synthesis of nanoparticles is environment friendly, less toxic and cost effective process. Plants, microorganisms, and biomolecules are commonly exploited species for merging of nanoparticles in this method. In present work we synthesize Chromium oxide nanoparticles by biological method using fungal extract of Aspargillus Niger. The synthesized nanoparticles are characterized by XRD (X-Ray Diffraction), SEM (Scanning Electron Microscopy) and UV-Vis (Ultraviolet Visible) techniques.

Boundedness of Littlewood-Paley Operators with Variable Kernel on Weighted Herz Spaces with Variable Exponent

EASL-Vol. 1 (2018), Issue 2, pp. 10–22 | Open Access Full-Text PDF

Afif Abdalmonem, Omer Abdalrhman, Shuangping Tao

Abstract:Let $\Omega\in{L}^{\infty}(\mathbb{R}^{n})\times{L^{2}(S^{n-1})}$ be a homogeneous function of degree zero. In this article, we obtain some boundedness of the parameterized Littlewood-Paley operators with variable kernels on weighted Herz spaces with variable exponent.

Global solution and asymptotic behaviour for a wave equation type $p$-laplacian with memory

OMA-Vol. 2 (2018), Issue 2, pp. 156–171 | Open Access Full-Text PDF

Carlos Alberto Raposo, Adriano Pedreira Cattai, Joilson Oliveira Ribeiro

Abstract:In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation
\begin{eqnarray*}
u_{tt} – \Delta_{p} u = \Delta u – g*\Delta u
\end{eqnarray*}
where $\Delta_{p} u$ is the nonlinear $p$-Laplacian operator, $p \geq 2$ and $g*\Delta u$ is a memory damping. The global solution is constructed by means of the Faedo-Galerkin approximations taking into account that the initial data is in appropriated set of stability created from the Nehari manifold and the asymptotic behavior is obtained by using a result of P. Martinez based on new inequality that generalizes the results of Haraux and Nakao.

Identification of a diffusion coefficient in degenerate/singular parabolic equations from final observation by hybrid method

OMA-Vol. 2 (2018), Issue 2, pp. 142–155 | Open Access Full-Text PDF

Khalid Atifi, El-Hassan Essoufi, Hamed Ould Sidi

Abstract:This paper deals with the determination of a coefficient in the diffusion term of some degenerate /singular one-dimensional linear parabolic equation from final data observations. The mathematical model leads to a non convex minimization problem. To solve it, we propose a new approach based on a hybrid genetic algorithm (married genetic with descent method type gradient). Firstly, with the aim of showing that the minimization problem and the direct problem are well posed, we prove that the solution’s behavior changes continuously with respect to the initial conditions. Secondly, we chow that the minimization problem has at least one minimum. Finally, the gradient of the cost function is computed using the adjoint state method. Also we present some numerical experiments to show the performance of this approach.

Analytic study on hilfer fractional langevin equations with impulses

OMA-Vol. 2 (2018), Issue 2, pp. 129–141 | Open Access Full-Text PDF

S. Harikrishnan, E. M. Elsayed, K. Kanagarajan

Abstract: In this paper, we find a solution of a new type of Langevin equation involving Hilfer fractional derivatives with impulsive effect. We formulate sufficient conditions for the existence and uniqueness of solutions. Moreover, we present Hyers-Ulam stability results.