Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
46 results
Search Results
Article Citation - Scopus: 10Third-Order Neutral Differential Equations of the Mixed Type: Oscillatory and Asymptotic Behavior(American Institute of Mathematical Sciences, 2022) Qaraad, B.; Moaaz, O.; Baleanu, D.; Santra, S.S.; Ali, R.; Elabbasy, E.M.In this work, by using both the comparison technique with first-order differential inequalities and the Riccati transformation, we extend this development to a class of third-order neutral differential equations of the mixed type. We present new criteria for oscillation of all solutions, which improve and extend some existing ones in the literature. In addition, we provide an example to illustrate our results. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)Article -Simultaneous chemometric determination of pyridoxine hydrochloride and isoniazid in tablets bymultivariate regression methods(Wiley-Blackwell, 2010) Dinç, Erdal; Üstündağ, Ögür; Baleanu, DumitruThe sole use of pyridoxine hydrochloride during treatment of tuberculosis gives rise to pyridoxine deficiency. Therefore, a combination of pyridoxine hydrochloride and isoniazid is used in pharmaceutical dosage form in tuberculosis treatment to reduce this side effect. In this study, two chemometric methods, partial least squares (PLS) and principal component regression (PCR), were applied to the simultaneous determination of pyridoxine (PYR) and isoniazid (ISO) in their tablets. A concentration training set comprising binary mixtures of PYR and ISO consisting of 20 different combinations were randomly prepared in 0.1 M HCl. Both multivariate calibration models were constructed using the relationships between the concentration data set (concentration data matrix) and absorbance data matrix in the spectral region 200-330 nm. The accuracy and the precision of the proposed chemometric methods were validated by analyzing synthetic mixtures containing the investigated drugs. The recovery results obtained by applying PCR and PLS calibrations to the artificial mixtures were found between 100.0 and 100.7%. Satisfactory results obtained by applying the PLS and PCR methods to both artificial and commercial samples were obtained. The results obtained in this manuscript strongly encourage us to use them for the quality control and the routine analysis of the marketing tablets containing PYR and ISO drugs. CopyrightArticle Citation - Scopus: 11Oscillation Result for Half-Linear Delay Di Erence Equations of Second-Order(American Institute of Mathematical Sciences, 2022) Santra, S.S.; Baleanu, D.; Edwan, R.; Govindan, V.; Murugesan, A.; Altanji, M.; Jayakumar, C.In this paper, we obtain the new single-condition criteria for the oscillation of secondorder half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results. © 2022 the Author(s), licensee AIMS Press.Article Citation - Scopus: 8Odd-Order Differential Equations With Deviating Arguments: Asymptomatic Behavior and Oscillation(American Institute of Mathematical Sciences, 2022) Muhib, A.; Dassios, I.; Baleanu, D.; Santra, S.S.; Moaaz, O.Despite the growing interest in studying the oscillatory behavior of delay differential equations of even-order, odd-order equations have received less attention. In this work, we are interested in studying the oscillatory behavior of two classes of odd-order equations with deviating arguments. We get more than one criterion to check the oscillation in different methods. Our results are an extension and complement to some results published in the literature. © 2022 the Author(s), licensee AIMS Press.Article Citation - WoS: 7Citation - Scopus: 6Novel Stochastic Dynamics of a Fractal-Fractional Immune Effector Response To Viral Infection Via Latently Infectious Tissues(Amer inst Mathematical Sciences-aims, 2022) Ashraf, Rehana; Asif, Qurat-Ul-Ain; Jarad, Fahd; Rashid, SaimaIn this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existenceuniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of nonnegative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-BaleanuCaputo derivative incorporating fractional-order alpha and fractal-dimension P have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.Article Citation - WoS: 9Citation - Scopus: 9New Classifications of Monotonicity Investigation for Discrete Operators With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2022) Goodrich, Christopher S.; Brzo, Aram Bahroz; Baleanu, Dumitru; Hamed, Yasser S.; Mohammed, Pshtiwan OthmanThis paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The v-monotonicity definitions, namely v-(strictly) increasing and v-(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with v-monotonicity definitions, we find that the investigated discrete fractional operators will be v(2)-(strictly) increasing or v(2)-(strictly) decreasing in certain domains of the time scale Na:= {a, a + 1, ... }. Finally, the correctness of developed theories is verified by deriving mean value theorem in discrete fractional calculus.Article Citation - WoS: 2Existence of Measure Pseudo-Almost Automorphic Functions and Applications To Impulsive Integro-Differential Equation(Aip Publishing, 2021) Baleanu, Dumitru; George, Soumya; Grayna, J.; Kavitha, V.This article's main objective is to establish the measure pseudo-almost automorphic solution of an integro-differential equation with impulses. We develop the existence results based on the Banach contraction principle mapping and Krasnoselskii and Krasnoselskii-Schaefer type fixed point theorems. Finally, some examples are given to illustrate the significance of our theoretical findings.Published under an exclusive license by AIP PublishingArticle Citation - WoS: 1Citation - Scopus: 1Analytical Results for Positivity of Discrete Fractional Operators With Approximation of the Domain of Solutions(Amer inst Mathematical Sciences-aims, 2022) O'Regan, Donal; Baleanu, Dumitru; Hamed, Y. S.; Elattar, Ehab E.; Mohammed, Pshtiwan OthmanWe study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 0 and epsilon > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of epsilon and theta.Article Citation - WoS: 12Citation - Scopus: 11A Computational Study of a Stochastic Fractal-Fractional Hepatitis B Virus Infection Incorporating Delayed Immune Reactions Via the Exponential Decay(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Al Qurashi, MaysaaRecently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order delta with constant fractal-dimension pi, delta with changing pi, and delta with changing both delta and pi. White noise concentration has a significant impact on how bacterial infections are treated.Article Citation - WoS: 17Citation - Scopus: 19New Numerical Dynamics of the Fractional Monkeypox Virus Model Transmission Pertaining To Nonsingular Kernels(Amer inst Mathematical Sciences-aims, 2023) Rashid, Saima; Alshehri, Ahmed M.; Jarad, Fahd; Safdar, Farhat; Al Qurashi, Maysaa; Qurashi, Maysaa AlMonkeypox (MPX) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system's equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system's disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus's transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.