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The widespread use of computer hardware and software in society has led to the emergence of a type of criminal conduct known as cybercrime, which has become a major worldwide concern in the 21st century spanning multiple domains. As a result, in the present setting, academics and practitioners are showing a great deal of interest in conducting research on cybercrime. In this work, a fractional-order model was replaced by involving three sorts of human populations: online computer users, hackers, and cyber security professionals, in order to examine the online computer user-hacker system. The existence, uniqueness and boundedness were studied. To support our theoretical conclusions, a numerical analysis of the influence of the various logical parameters was conducted and we derived the necessary conditions for the different equilibrium points to be locally stable. We examined the effects of the fear level and refuge factor on the equilibrium densities of prey and predators in order to explore and understand the dynamics of the system in a better way. Using some special circumstances, the model was examined. Our theoretical findings and logical parameters were validated through a numerical analysis utilizing the generalized Adams-Bashforth-Moulton technique.

Abstract In this paper, we provide some appropriate conditions for the existence of solutions for a perturbed fractional neutral integro-differential system under the deformable derivative in a Banach space. Using the Banach contraction principle and Krasnoselskii’s fixed point theorem, we establish some new existence theorems. Moreover, we provide two numerical examples to demonstrate the applicability of the theoretical results

Abstract The present research work investigates some new results for a fractional generalized Sturm–Liouville–Langevin (FGSLL) equation involving the Ψ-Caputo fractional derivative with a modified argument. We prove the uniqueness of the solution using the Banach contraction principle endowed with a norm of the Ψ-Bielecki-type. Meanwhile, the fixed-point theorems of the Leray–Schauder and Krasnoselskii type associated with the Ψ-Bielecki-type norm are used to derive the existence properties by removing some strong conditions. We use the generalized Gronwall-type inequality to discuss Ulam–Hyers (UH), generalized Ulam–Hyers (GUH), Ulam–Hyers–Rassias (UHR), and generalized Ulam–Hyers–Rassias (GUHR) stability of these solutions. Lastly, three examples are provided to show the effectiveness of our main results for different cases of (FGSLL)-problem such as Caputo-type Sturm–Liouville, Caputo-type Langevin, Caputo–Erdélyi–Kober-type Langevin problems.

Değişen tüketici davranışları yemek tüketimine de yansımış ve günümüzde tüketiciler internet üzerinden yemek siparişi vermeye başlamıştır. Tüketiciler yemek siparişlerini, online yemek sipariş hizmeti sunan işletmelerin web sitesi ve mobil uygulamaları üzerinden verebilmektedir. Araştırmanın amacı web sitesi ya da mobil uygulamalar üzerinden yemek siparişi vermiş olan tüketicilerin algıladıkları değer, güven ve promosyonun elektronik kulaktan kulağa pazarlama davranışı üzerindeki etkisini ortaya çıkarmaktır. Nicel araştırma yönteminin tercih edildiği araştırmada, anket tekniği kullanılmış ve veriler tesadüfi olmayan örneklem yöntemlerinden kolayda örneklem yöntemi ile elde edilmiştir. Bu doğrultuda veriler daha önce online yemek siparişi vermiş olan tüketicilerden Kasım-Aralık (2023) aylarında online olarak toplanmıştır. Elde edilen veriler SPSS 25 ve AMOS 24 istatistik paket programları ile analiz edilmiştir. Yapılan analiz sonucunda online yemek siparişi hizmeti sunan web sitesi ve mobil uygulamalarla ilgili algılanan değer, güven ve promosyonun elektronik kulaktan kulağa pazarlama davranışı üzerinde pozitif yönde anlamlı etkilerinin olduğu belirlenmiştir. Elde edilen sonuçlar hem teorik hem de uygulamaya yönelik önemli katkılar sağlamaktadır.

The summation and exact form of the solutions related to the special type of difference equations are established in this paper by using the inverse of the delta and alpha-delta operators. As an application, the solutions of the population growth model, particularly, fractional order kinetic equation, are obtained by this method. Also, by using the summation form and Mittag–Leffler factorial functions, the alpha-delta integrations have been applied for solving the fractional order difference equations involving the factorial polynomials. Numerical examples are provided to validate the theoretical results.

In the present article, the matrix projective synchronization (MPS) and the inverse matrix projective synchronization (IMPS) have been analyzed with fractional-order chaotic systems with uncertain terms. First, we theoretically discussed both types of synchronizations. To achieve both types of synchronization, several required conditions are derived. We also drew portraits of Lyapunov’s exponents and bifurcation for more analysis. Furthermore, time-delay terms are also considered, giving an elegant application in real-world problems. Finally, numerical results agreed with the theoretical hypothesis. The numerical outcomes are shown through the graphical presentation.

The World Health Organization declared COVID-19 a global pandemic in March 2020, which had a significant impact on global health and economies. There have been several Zika outbreaks in different regions such as Africa, Southeast Asia, and the Americas. Therefore, it is essential to study the dynamics of these two diseases, taking into account their memory and recurrence effects. A new fractal-fractional hybrid Mittag-Leffler model of COVID-19 and Zika co-dynamics is designed and studied to evaluate the effects of COVID-19 on Zika and vice-versa. The stability analysis of the local asymptotic type at disease-free equilibrium is conducted for the hybrid model. The existence of unique solutions to the model is established via some fixed point results. The fractal-fractional model is proved to be Hyers–Ulam stable. With the help of Newton polynomials, we obtain some numerical algorithms to approximate the solutions of the fractal-fractional hybrid Mittag-Leffler model graphically. The impact of fractional and fractal orders on the dynamics of each of the epidemiological classes is also assessed. In addition, empirical evidence from numerical simulations suggests that implementing measures to contain the transmission of the SARS-CoV-2 virus can significantly contribute to the reduction of co-infections involving the Zika virus. Therefore, it is imperative for healthcare systems to maintain a state of constant vigilance in order to detect any atypical patterns or probable occurrences of co-infections, particularly in areas where both diseases are widespread. Additionally, it is vital to consult the most recent directives provided by health authorities, as our comprehension of diseases may undergo advancements over the course of time.

SARS-CoV-2 is a strain of the large coronavirus family that has led to COVID-19 disease. The virus has been one of the deadliest known viruses in the world to date. Rapid mutations and the creation of new strains cause researchers to focus on the dynamic behaviors of the virus and to analyze it accurately through clinical research and mathematical models. In this paper, from the point of view of mathematical modeling, we intend to focus on the dynamic behavior of the system and examine its analytical and numerical aspects in two different structures. In other words, by recalling newly formulated hybrid fractional-fractal operators, we present a fractal-fractional probability-based model of SARS-CoV-2 virus for the first time and extract its equivalent compact fractal-fractional IVP to investigate its existence and stability criteria. A type of special admissible contractions will help us in this regard. Moreover, based on the source data, we simulate our system according to algorithms derived by Adams-Bashforth method and explain the effects of variation of the dimension of fractal and fractional order on dynamics of solutions. Finally, we transform our fractal-fractional model into a Caputo probability-based model of SARS-CoV-2 to derive solutions via the operational matrix method under Taylor’s basis. The numerical simulations show close behaviors for both of models.

In this paper, a new kind of mathematical modeling is studied by providing a five-compartmental system of differential equations with respect to new hybrid generalized fractal-fractional derivatives. For the first time, we design a model of giving up smoking to analyze its dynamical behaviors by considering two parameters of such generalized operators; i.e., fractal dimension and fractional order. We apply a special sub-category of increasing functions to investigate the existence of solutions. Uniqueness property is derived by a standard method based on the Lipschitz rule. After proving stability property, the equilibrium points are obtained and asymptotically stable solutions are studied. Finally, we illustrate all analytical results and findings via numerical algorithms and graphs obtained by Lagrangian piece-wise interpolation, and discuss all behaviors of the relevant solutions in the fractal-fractional system.

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures.

In this article, we propose a numerical method based on the fractional Taylor vector for solving multi-term fractional differential equations. The main idea of this method is to reduce the given problems to a set of algebraic equations by utilizing the fractional Taylor operational matrix of fractional integration. This system of equations can be solved efficiently. Some numerical examples are given to demonstrate the accuracy and applicability. The results show that the presented method is efficient and applicable.

Purpose – The present research study extends the Expectation-Confirmation Model (ECM) by focusing on satisfaction, continuance intention, and recommendation intention among smart robotic vacuum cleaner users. The impacts of battery life concern and perceived privacy factors on satisfaction and continuance intention of the smart robotic vacuum cleaner were investigated by adding the variables of battery life concern, perceived privacy, and recommendation intention in the ECM. Design/methodology/approach – The participants of this study consisted of smart robotic vacuum cleaner users in Turkey. The snowball sampling method, as one of the non-random sampling methods, was used to reach the participants; data was collected using an online survey created with Google Forms, asking the participants to share the survey link with people around them who have smart robotic vacuum cleaners. A total of 218 smart robotic vacuum cleaner users participated in the study between March 1 and May 1, 2023. Findings and implications – Structural equation modeling (SEM) was used as the data analysis technique in the study. While the ECM was confirmed as a result of the SEM analysis, an important finding was that consumers with battery life concerns intend to continue using the smart robotic vacuum cleaner despite a negative relationship between battery life concern and satisfaction. While the effect of perceived privacy on continuance intention was not significant, satisfaction was found to have a significant effect on continuance intention. Given that artificial intelligence-related businesses face fierce competition, organizations that wish to prosper in this environment must excel in a variety of areas, ranging from product design to marketing and from sales policies to post-sales assistance. Considering the findings, determining the factors that affect the satisfaction and intention to continue using robot vacuum cleaners will be a guide for smart robot vacuum cleaner manufacturers and marketers. At the same time, the fact that the issue has been investigated within the framework of a model will also make significant contributions to the literature. Limitations – Different factors influence smart robotic vacuum cleaner users’ satisfaction and desire to continue using them, but only battery-life concerns and perceived privacy variables were incorporated into the ECM model in this research study. Another limitation is connected to the research sample. Because the snowball sampling method was employed to obtain data for the research, its findings cannot be generalized as they cover only smart robotic vacuum cleaner users who participated in the survey. Originality/value – The ECM employed in the study was expanded by including the variables of battery-life concern, perceived privacy, and recommendation intention. A general lack of information among potential consumers regarding artificial intelligence and smart robotic vacuum cleaners, which is highly fascinating and a source of curiosity, as well as the lack of research on this issue in the literature, underscore the significance of this research study. By integrating and expanding the ECM for application to consumers using smart robotic vacuum cleaners, this study adds a fresh viewpoint to the literature.

Araştırmanın amacı sağlık bilinci, çevre endişesi, ürün güvenliği ile sosyal ve kişisel normların tüketicilerin organik ürün satın alma niyetleri üzerinde etkilerini ve organik ürün satın alma niyetinin de gerçek satın alma ve tekrar satın alma niyeti üzerinde etkilerini belirlemektir. Araştırmanın ana evreni Gümüşhane ilinde yaşayan ve organik ürün tüketen tüketicilerdir. Kolayda örneklem yöntemi tercih edilerek hazırlanan anket formu ile 473 tüketiciye ulaşılmıştır. Elde edilen veriler SPSS ve AMOS programları ile analiz edilmiş ve sağlık bilinci, gıda güvenliği, kişisel ve sosyal normların satın alma niyeti üzerinde, satın alma niyetinin de gerçek ve tekrar satın alma niyetleri üzerinde olumlu etkisinin olduğu belirlenmiştir. Ayrıca çevre endişesi faktörünün satın alma niyeti üzerinde herhangi bir etkisinin olmadığı araştırmada elde edilen diğer bir sonuçtur. Ulaşılan bu sonuçlar organik ürünlerle ilgili literatüre önemli katkılar sağlamaktadır.