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The objective of this manuscript is to present a novel approach to modeling influenza A disease dynamics by incorporating the Caputo-Fabrizio (CF) fractional derivative operator into the model. Particularly distinct contact rates between exposed and infected individuals are taken into account in the model under study, and the fractional derivative concept is explored with respect to this component. We demonstrate the existence and uniqueness of the solution and obtain the series solution for all compartments using the Laplace transform method. The reproduction number of the Influenza A model, which was created to show the effectiveness of different contact rates, was obtained and examined in detail in this sense. To validate our approach, we applied the predictor-corrector method in the sense of the Caputo-Fabrizio fractional derivative and demonstrate the effectiveness of the fractional derivative in accurately predicting disease dynamics. Our findings suggest that the use of the Caputo-Fabrizio fractional derivative can provide valuable insights into the mechanisms underlying influenza A disease and enhance the accuracy of disease models.

Geometric properties of finite Blaschke products have been intensively studied by many different aspects. In this paper, our aim is to study geometric properties of finite Blaschke products related to the golden ratio $\alpha =\frac{1+\sqrt{5}}{2}$. Mainly, we focus on the relationships between the zeros of canonical finite Blaschke products of lower degree and the golden ratio. We show that the geometric notions such as "golden triangle, "golden ellipse" and "golden rectangle" are closely related to the geometry of finite Blaschke products.

Plant growth and development are regulated by light, which is a significant environmental component. It is involved in seedling de-etiolation, phototropism, shadow escaping, seed germination, circadian rhythms, and blooming timing, among other reactions in the plant life cycle (collectively termed photomorphogenesis). These light responses are controlled by phytochromes, which interact with a variety of partner proteins. The purpose of this study was to identify and describe members of the phytochrome-interacting factors (PIFs) gene family including the basic helix loop helix (bHLH) binding site in Phaseolus vulgaris plants, as well as to investigate their responses to salt and drought stress. Various tools in silico approaches were used to identify five Pvul-PIF gene families in the P. vulgaris genome. This gene family contained 324 to 726 amino acids and has molecular weights ranging from 35.11 kDa to 77.67 kDa. The theoretical isoelectric points range from 6.03 (Pvul-PIF-3.3) to 8.30 (Pvul-PIF-3.2). Pvul-PIF proteins were shown to be clustered in three main groups with Arabidopsis thaliana, Populus trichocarpa, Solanum lycopersicum, Zea mays, Arachis hypogaea L., Oryza sativa, Vitis vinifera, Glycine max, and Phaseolus vulgaris species as a result of the phylogenetic study. Segmental duplication was detected between Pvul-PIF-3.2, Pvul-PIF-3.3 and Pvul-PIF-3.1 genes, Pvul-PIF-4.1 and Pvul-PIF-4.2 genes and Pvul-PIF-3.3 and Pvul-PIF-3.1 genes. When the expression patterns of the Pvul-PIF genes were examined, it was observed that they had different levels of expression under salt and drought stress and that they may be involved in specific biological and molecular processes in response to different abiotic and biotic stresses. The results of this research, which were established for the first time in the response to salt and drought stress in P. vulgaris of the PIF gene family, will be a valuable source of knowledge and additional information in the fields of plant biotechnology, agricultural biotechnology, and molecular biology.

In this paper, we present the complex Rolle’s and Mean Value Theorems for $$\alpha$$ -holomorphic functions and give some related results and applications of these theorems.

Infectious diseases have caused the death of many people throughout the world for centuries. For this purpose, many researchers have investigated these diseases for establishing new treatment and protective measures. The most important of these is HIV disease. In this study, an HIV infection model of CD4+ T cells is handled comprehensively with the newly defined Atangana-Baleanu (AB) fractional derivative. The existence and uniqueness of the solutions for fractionalized HIV disease model with the new derivative by considering the Arzela-Ascoli theorem.

The kill signals are alert about possible viruses that infect computer network to decrease the danger of virus propagation. In this work, we focus on a fractional-order SEIR-KS model in the sense of Caputo derivative to analyze the effects of kill signal nodes on the virus propagation. For this purpose, we first prove the existence and uniqueness of the model and give qualitative analysis. Then, we obtain the numerical solution of the model by using the Adams–Bashforth–Moulton algorithm. Finally, the effects of model parameters are demonstrated with graphics drawn by MATLAB program.

Uçar, Sümeyra (Balikesir Author), Nonlinear fractional differential equations have been intensely studied using fixed point theorems on various different function spaces. Here we combine fixed point theory with complex analysis, considering spaces of analytic functions and the behaviour of complex powers. It is necessary to study carefully the initial value properties of Riemann–Liouville fractional derivatives in order to set up an appropriate initial value problem, since some such problems considered in the literature are not well-posed due to their initial conditions. The problem that emerges turns out to be dimensionally consistent in an unexpected way, and therefore suitable for applications too. © 2021, The Author(s).

Diabetes mellitus, at the forefront of the diseases of our age, is a type of disease that plays a leading role in the formation of many deadly diseases and is very common all over the world. In this work, based on the system in Shabestari et al. (Chaos Solitons Fractals 112:44–51, 2018), we give the fractional glucose–insulin regulatory system for the first time by Caputo–Fabrizio derivative. We present special solutions, stability analysis, uniqueness of the solution for this fractional system with the aid of Banach fixed point theory. Taking various values belonging to the fractional order into consideration, we present some numerical results according to the relation between glucose, insulin and $$\beta $$ -cells.

A computer virus is actually a kind of computer program that changes the operation of the computer and tries to hide itself in other files without the user's consent or knowledge. In this paper we deal with a computer virus spreading model benefiting from Atangana-Baleanu derivative in Caputo sense with non- local and non- singular kernels. The solution properties of our fractional model are established benefiting from Arzelo-Ascoli theorem.

Uçar, Sümeyra (Balikesir Author), In this study, we introduce a new complex conformable derivative and integral with noninteger order which coincides the classical complex derivative and integral for = 1. We examine basic properties of these newly defined derivative and integral such as Cauchy-Riemann equations, conformability and fundamental theorem of complex conformable integral. As an application of the new operators, we solve some types of complex conformable differential equations., Balikesir University - Bap 2018/023

Bu çalışmada elemanları genelleştirilmiş Fibonacci ve Lucas polinomları olan devirsel matrisler kullanılarak iki yeni kodlama algoritması vereceğiz. Bu amaçla, genelleşirilmiş Fibonacci polinomları, genelleştirilmiş Lucas polimomları ve geometrik diziler kullanılarak sağ devirsel matrislerin bazı temel özelliklerini çalışacağız., In the present paper, we consider two new coding algorithms by means of right circulant matrices with elements generalized Fibonacci and Lucas polynomials. To that end, we study basic properties of right circulant matrices using generalized Fibonacci polynomials, generalized Lucas polynomialsand geometric sequences.

Let $B(z)$ be a finite Blaschke product of degree $n$. We consider the problem when a finite Blaschke product can be written as a composition of two nontrivial Blaschke products of lower degree related to the condition $% B\circ M=B$ where $M$ is a M\"{o}bius transformation from the unit disk onto itself.

Uçar, Sümeyra (Balikesir Author), This paper ensures meticulous mathematical study for analyzing the dynamics of smoking model and its public health with Atangana-Baleanu derivative. The existence and uniqueness problems to relevant model are examined via fixed point theory. The results are implemented by giving some illustrative graphics including the variation of fractional order. (C) 2018 Elsevier Ltd. All rights reserved.

Evirgen, Fırat (Balikesir Author), In this study, we aim to comprehensively investigate a drinking model connected to immigration in terms of Atangana-Baleanu derivative in Caputo type. To do this, we firstly extend the model describing drinking model by changing the derivative with time fractional derivative having Mittag-Leffler kernel. The existence and uniqueness of the drinking model solutions together with the stability analysis is shown by the help of Banach fixed point theorem. The special solution of the model is investigated using the Sumudu transformation and then, we present some numerical simulations for the different fractional orders to emphasize the effectiveness of the used derivative.

These days, it is widely known that smoking causes numerous diseases, as well as resulting in many avoidable losses of life globally, and therefore encumbers the society with enormous unnecessary burdens. The aim of this study is to examine in-depth a smoking model that is mainly influenced by determination and educational actions via CF and AB derivatives. For both fractional order models, the fixed point method is used, which allows us to follow the proof of existence and the results of uniqueness. The effective properties of the above-mentioned fractional models are theoretically exhibited, their results are confirmed by numerical graphs by various fractional orders. 1. Introduction. Today, it is widely recognized that smoking does not bring about any benefits; on the contrary, each and every segment of the society is now aware of the numerous hazards that smoking engenders. For instance, your skin becomes deprived of moisture and elasticity, you become more likely to suffer from hypertension, your DNA becomes prone to detrimental effects, your immune system is rendered weaker, and you come face to face with worrisome issues involving economy, pregnancy, overall health, risk of untimely death, and so on. Moreover, many types of cancer, such as lung, mouth, and throat cancers take their source from the hazardous but often-unseen impact of smoking on our health according to researchers. In brief, the hazards originating from the smoking habit result in serious complications in both individual and social spheres. It has been formidably anticipated that no fewer than 7 million people lose their lives due to smoking-related problems every year worldwide. Taking all of these unfavorable facts into consideration, scientists from a multitude of fields seek to vanquish this dangerous habit so that they may expect to extend the health span of human beings. And many of those researchers concentrate on mathematical models to demonstrate the most., Balikesir University Bap 2019/099

Coding/decoding algorithms are of great importance to help in improving information security since information security is a more significant problem in recent years. In this paper we introduce two new coding/decoding algorithms using Fibonacci Q-matrices and R-matrices. Our models are based on the blocked message matrices and the encryption of each message matrix with different keys. These new algorithms will not only increase the security of information but also has high correct ability.

In this paper we present a new method of coding/decoding algorithms using Fibonacci $Q$-matrices. This method is based on the blocked message matrices. The main advantage of our model is the encryption of each message matrix with different keys. Our approach will not only increase the security of information but also has high correct ability., Comment: 10 pages, 2 tables. arXiv admin note: substantial text overlap with arXiv:1709.10355