Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 3Alternative Approaches To the Spectral Quantitative Resolution of Two-Component Mixture by Wavelet Families(Soc Chilena Quimica, 2009) Dinc, Erdal; Baleanu, Dumitru; Arslan, Fahrettin; Baleanu, Dumitru; MatematikA new spectral continuous wavelet transform (CWT) methods are proposed for the quantitative analysis of the binary mixtures. The simultaneous spectral resolution of binary mixtures and tablets containing paracetamol (PAR) and chloroxozone (CHL) with overlapping absorption spectra is performed by six wavelet families with no chemical separation procedure. The calibration graphs for the six wavelet families are obtained by the help of the data collected from the CWT-signal amplitudes corresponding to the zero crossing points in the spectral range of 210 nm-310 nm. The validation of each wavelet family is carried out by analyzing various synthetic binary mixtures of the above mentioned drugs. The second derivative spectrophotometry (D2) is used to compare the experimental results provided by the analyzed continuous wavelet families and a good coincidence is reported for the proposed analytical approaches.Article Citation - WoS: 1Citation - Scopus: 2On the Complementary Nabla Pachpatte Type Dynamic Inequalities Via Convexity(Elsevier, 2024) Kaymakcalan, Billur; Kayar, ZeynepPachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to develop certain branches of mathematics such as fuctional analysis, operator theory, optimization and ordinary/partial differential equations. We extend classical nabla Pachpatte type dynamic inequalities by changing the interval of the exponent delta from delta > 1 to delta < 0. Our results not only complement the classical nabla Pachpatte type inequalities but also generalize complementary nabla Hardy-Copson type inequalities. As the case of delta < 0 has not been previously examined, these complementary inequalities represent a novelty in the nabla time scale calculus, specialized cases in continuous and discrete scenarios, and in the dual outcomes derived in the delta time scale calculus.Article Citation - Scopus: 2Quadruple Best Proximity Points With Applications To Functional and Integral Equations(Wiley, 2022) Rashwan, Rashwan A.; Nafea, A.; Jarad, Fahd; Hammad, Hasanen A.This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.Article Citation - Scopus: 14The Effect of Deformation of Special Relativity by Conformable Derivative(Sociedad Mexicana de Fisica, 2022) Al-Masaeed, M.; Rabei, E.M.; Baleanu, D.; Al-Jamel, A.In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium. © 2022, Revista Mexicana de Fisica. All Rights Reserved.Article Citation - WoS: 6The Complementary Nabla Bennett-Leindler Type Inequalities(Ankara Univ, Fac Sci, 2022) Kayar, Zeynep; Kaymakcalan, BillurWe aim to find the complements of the Bennett-Leindler type inequalities in nabla time scale calculus by changing the exponent from 0 < zeta < 1 to zeta > 1. Different from the literature, the directions of the new inequalities, where zeta > 1, are the same as that of the previous nabla Bennett-Leindler type inequalities obtained for 0 < zeta < 1. By these settings, we not only complement existing nabla Bennett-Leindler type inequalities but also generalize them by involving more exponents. The dual results for the delta approach and the special cases for the discrete and continuous ones are obtained as well. Some of our results are novel even in the special cases.Article Citation - WoS: 6Citation - Scopus: 9Neutral Functional Sequential Differential Equations With Caputo Fractional Derivative on Time Scales(Springernature, 2022) Lazreg, Jamal Eddine; Benkhettou, Nadia; Benchohra, Mouffak; Karapinar, ErdalIn this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray-Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.Article Citation - WoS: 5Citation - Scopus: 5Stochastic Epidemic Model of Covid-19 Via the Reservoir-People Transmission Network(Tech Science Press, 2022) Fahimi, Milad; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, KazemThe novel Coronavirus COVID-19 emerged in Wuhan, China in December 2019. COVID-19 has rapidly spread among human populations and other mammals. The outbreak of COVID-19 has become a global challenge. Mathematical models of epidemiological systems enable studying and predicting the potential spread of disease. Modeling and predicting the evolution of COVID-19 epidemics in near real-time is a scientific challenge, this requires a deep understanding of the dynamics of pandemics and the possibility that the diffusion process can be completely random. In this paper, we develop and analyze a model to simulate the Coronavirus transmission dynamics based on Reservoir-People transmission network. When faced with a potential outbreak, decision-makers need to be able to trust mathematical models for their decision-making processes. One of the most considerable characteristics of COVID-19 is its different behaviors in various countries and regions, or even in different individuals, which can be a sign of uncertain and accidental behavior in the disease outbreak. This trait reflects the existence of the capacity of transmitting perturbations across its domains. We construct a stochastic environment because of parameters random essence and introduce a stochastic version of the Reservoir-People model. Then we prove the uniqueness and existence of the solution on the stochastic model. Moreover, the equilibria of the system are considered. Also, we establish the extinction of the disease under some suitable conditions. Finally, some numerical simulation and comparison are carried out to validate the theoretical results and the possibility of comparability of the stochastic model with the deterministic model.Article Citation - WoS: 4Citation - Scopus: 6Extensions of Meir-Keeler Contraction Via W-Distances With an Application(Univ Kragujevac, Fac Science, 2022) Karapinar, Erdal; Lakzian, Hosein; Chanda, Ankush; Barootkoob, SedighehIn this article, we conceive the notion of a generalized (alpha, psi, q)-Meir-Keeler contractive mapping and then we investigate a fixed point theorem involving such kind of contractions in the setting of a complete metric space via a w-distance. Our obtained result extends and generalizes some of the previously derived fixed point theorems in the literature via w-distances. In addition, to validate the novelty of our findings, we illustrate a couple of constructive numerical examples. Moreover, as an application, we employ the achieved result to earn the existence criteria of the solution of a kind of non-linear Fredholm integral equation.Article Citation - WoS: 3Citation - Scopus: 3Examination of Pine Wilt Epidemic Model Through Efficient Algorithm(Tech Science Press, 2022) Mahmoud, Emad E.; Al-Bugami, A. M.; Baleanu, Dumitru; Rafiq, Muhammad; Mohsin, Muhammad; Al Nuwairan, Muneerah; Raza, Ali; Nuwairan, Muneerah AlPine wilt is a dramatic disease that kills infected trees within a few weeks to a few months. The cause is the pathogen Pinewood Nematode. Most plant-parasitic nematodes are attached to plant roots, but pinewood nematodes are found in the tops of trees. Nematodes kill the tree by feeding the cells around the resin ducts. The modeling of a pine wilt disease is based on six compartments, including three for plants (susceptible trees, exposed trees, and infected trees) and the other for the beetles (susceptible beetles, exposed beetles, and infected beetles). The deterministic modeling, along with subpopulations, is based on Law of mass action. The stability of the model along with equilibria is studied rigorously. The authentication of analytical results is examined through well-known computer methods like Non-standard finite difference (NSFD) and the model's feasible properties (positivity, boundedness, and dynamical consistency). In the end, comparison analysis shows the effectiveness of the NSFD algorithm.Article Citation - WoS: 12Citation - Scopus: 17Dynamics of Multi-Point Singular Fifth-Order Lane-Emden System With Neuro-Evolution Heuristics(Springer Heidelberg, 2022) Ali, Mohamed R.; Fathurrochman, Irwan; Raja, Muhammad Asif Zahoor; Sadat, R.; Baleanu, Dumitru; Sabir, ZulqurnainThe objective of the presented communication is to examine and analyze the solutions of nonlinear multi-singular fifth-order Lane-Emden (LE) system for different scenarios by variation of shape factors settled on the equivalent design of the LE equations. The neuro-evolution based stochastic computing is explored for the numerical measures using the artificial neural networks (ANNs) models for the appropriate continuous mapping, while the learning of decision variables is conducted using the integrated meta-heuristic global search of genetic algorithms (GA) hybrid with the local search efficiency of active-set (AS) i.e., ANN-GA-AS scheme. The numerical approach ANN-GA-AS is applied efficiently for the fifth kind of nonlinear LE model and statistical calculations further validate the accuracy, robustness as well as convergence.