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The paper outlines a self-contained scheme for multiple networking agents at a location. It proposes a mathematical model for intelligent cloud entropy management systems. The purpose of this paper is to minimize the cost of system functionality by proposing the substantial use of a cloud-based system.

The paper proposes a hybrid cloud system, based on a fractional calculus of hybrid integral systems. Its discrete dynamics are suggested by using the fractional entropy type known as Tsallis entropy. This approach is based on the Wiener process (i.e. diffusion processes). This involves the net movement of information or data from a state of high meditation to a state of low observation. This property is a basic characteristic of hybrid cloud computing systems.

The paper offers a number of solutions to minimize the costs of cloud systems. The method is a proficient technique for presenting various types of fractional differential solutions.

Researchers are encouraged to test and modify the proposed method.

The paper includes suggestions for the expansion of a powerful method for managing and integrating cloud systems stably.

This paper addresses an acknowledged need to study how the cost function of cloud systems can be achieved.

Phishing is a serious cybersecurity problem, which is widely available through multimedia, such as e-mail and Short Messaging Service (SMS) to collect the personal information of the individual. However, the rapid growth of the unsolicited and unwanted information needs to be addressed, raising the necessity of the technology to develop any effective anti-phishing methods.

The primary intention of this research is to design and develop an approach for preventing phishing by proposing an optimization algorithm. The proposed approach involves four steps, namely preprocessing, feature extraction, feature selection and classification, for dealing with phishing e-mails. Initially, the input data set is subjected to the preprocessing, which removes stop words and stemming in the data and the preprocessed output is given to the feature extraction process. By extracting keyword frequency from the preprocessed, the important words are selected as the features. Then, the feature selection process is carried out using the Bhattacharya distance such that only the significant features that can aid the classification are selected. Using the selected features, the classification is done using the deep belief network (DBN) that is trained using the proposed fractional-earthworm optimization algorithm (EWA). The proposed fractional-EWA is designed by the integration of EWA and fractional calculus to determine the weights in the DBN optimally.

The accuracy of the methods, naive Bayes (NB), DBN, neural network (NN), EWA-DBN and fractional EWA-DBN is 0.5333, 0.5455, 0.5556, 0.5714 and 0.8571, respectively. The sensitivity of the methods, NB, DBN, NN, EWA-DBN and fractional EWA-DBN is 0.4558, 0.5631, 0.7035, 0.7045 and 0.8182, respectively. Likewise, the specificity of the methods, NB, DBN, NN, EWA-DBN and fractional EWA-DBN is 0.5052, 0.5631, 0.7028, 0.7040 and 0.8800, respectively. It is clear from the comparative table that the proposed method acquired the maximal accuracy, sensitivity and specificity compared with the existing methods.

The e-mail phishing detection is performed in this paper using the optimization-based deep learning networks. The e-mails include a number of unwanted messages that are to be detected in order to avoid the storage issues. The importance of the method is that the inclusion of the historical data in the detection process enhances the accuracy of detection.

The purpose of this offered research is to articulate a multifaceted kind of highly unstable initial perturbation and further analyze the performance of the plasma particles for time-fractional order evaluation.

For this purpose, the authors designed specific geometry and further interpreted it into the mathematical model using the concepts of the Vlasov Maxwell system. The suggested algorithm is based on the finite-difference and spectral estimation philosophy. The management of time and memory in generic code for computational purposes is also discussed.

The main purpose is to analyze the fractional behavior of plasma particles and also the capability of the suggested numerical algorithm. Due to initial perturbations, there are a lot of sudden variations that occurred in the formulated system. Graphical behavior shows that SR parameter produces devastation as compared to others. The variation of fractional parameter between the defend domain demonstrates the hidden pictures of plasma particles. The design scheme is efficient, convergent and has the capability to cover the better physics of the problem.

Plasma material is commonly used in different areas of science. Therefore, in this paper, the authors increase the capability of the mathematical plasma model with specific geometry, and further suitable numerical algorithm is suggested with detailed physical analysis of the outcomes. The authors gave a new direction to study the performance of plasma particles under the influence of LASER light.

In the recent era, science has produced a lot of advancements to study and analyze the physical natural process, which exist everywhere in the real word. On behalf of this current developments, it is now insufficient to study the first-order time evaluation of the plasma particles. One needs to be more precise and should move toward the bottomless state of it, that is, macroscopic and microscopic time-evaluation scales, and it is not wrong to say that there exits a huge gap, to study the time evaluation in this discussed manner. The presented study is entirely an advanced and efficient way to investigate the problem into the new directions. The capability of the proposed algorithm and model with fractional concepts can fascinate the reader to extend to the other dimensions.

The purpose of this paper is to determine the profile of the typical online fractional residential property investor in Australia. This study also seeks to understand the motives for engaging with and investing in alternative residential property investments.

This study employs a survey-based design via an online questionnaire to gather information on investor age, gender, type, education levels, time horizons and investment history and risk and return expectations. It also gathers information regarding investors’ financial literacy including tax implications of fractional property investment.

The findings of this study suggest amongst others, that fractional property investors tend to be younger, although the platform also attracts older investors including older females. The study also found that investors do not select alternative investment platforms in anticipation of super-normal investment returns. Return expectations are realistic and are based on a balance between capital growth and income.

This study indicates that alternative investment platforms lowers the barriers of entry into residential property for first time investors. It therefore creates opportunities to allow many first time individual investors to invest in property, often as an alternative to bank savings or investing in the stock market.

This study enhances our understanding of the influence of alternative investment platforms on investment decision-making. More specifically, it contrasts fractional property investment with more traditional investment opportunities to understand the motives of investors for diversifying into online investment vehicles.

The classical integer derivative diffusionmodels for fluid flow within a channel of parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a quiescent Newtonian fluid within a circular pipe are initially generalized by introducing fractional derivatives. The purpose of this paper is to represent solutions as steady and transient parts. Afterward, making use of separation of variables, a fractional Sturm–Liouville eigenvalue task is posed whose eigenvalues and eigenfunctions enable us to write down the transient solution in the Fourier series involving also Mittag–Leffler function. An alternative solution based on the Laplace transform method is also provided.

In this work, an analytical formulation is presented concerning the transient and passage to steady state in fluid flow and heat transfer within the diffusion fractional models.

From the closed-form solutions, it is clear to visualize the start-up process of physical diffusion phenomena in fractional order models. In particular, impacts of fractional derivative in different time regimes are clarified, namely, the early time zone of acceleration, the transition zone and the late time regime of deceleration.

With the newly developing field of fractional calculus, the classical heat and mass transfer analysis has been modified to account for the fractional order derivative concept.

Vertical handoff mechanism (VHO) becomes very popular because of the improvements in the mobility models. These developments are less to certain circumstances and thus do not provide support in generic mobility, but the vertical handover management providing in the heterogeneous wireless networks (HWNs) is crucial and challenging. Hence, this paper introduces the vertical handoff management approach based on an effective network selection scheme.

This paper aims to improve the working principle of previous methods and make VHO more efficient and reliable for the HWN.Initially, the handover triggering techniques is modelled for identifying an appropriate place to initiate handover based on the computed coverage area of cellular base station or wireless local area network (WLAN) access point. Then, inappropriate networks are eliminated for determining the better network to perform handover. Accordingly, a network selection approach is introduced on the basis ofthe Fractional-dolphin echolocation-based support vector neural network (Fractional-DE-based SVNN). The Fractional-DE is designed by integrating Fractional calculus (FC) in Dolphin echolocation (DE), and thereby, modifying the update rule of the DE algorithm based on the location of the solutions in past iterations. The proposed Fractional-DE algorithm is used to train Support vector neural network (SVNN) for selecting the best weights. Several parameters, like Bit error rate (BER), End to end delay (EED), jitter, packet loss, and energy consumption are considered for choosing the best network.

The performance of the proposed VHO mechanism based on Fractional-DE is evaluated based on delay, energy consumption, staytime, and throughput. The proposed Fractional-DE method achieves the minimal delay of 0.0100 sec, the minimal energy consumption of 0.348, maximal staytime of 4.373 sec, and the maximal throughput of 109.20 kbps.

In this paper, a network selection approach is introduced on the basis of the Fractional-Dolphin Echolocation-based Support vector neural network (Fractional-DE-based SVNN). The Fractional-DE is designed by integrating Fractional calculus (FC) in Dolphin echolocation (DE), and thereby, modifying the update rule of the DE algorithm based on the location of the solutions in past iterations. The proposed Fractional-DE algorithm is used to train SVNN for selecting the best weights. Several parameters, like Bit error rate (BER), End to end delay (EED), jitter, packet loss, and energy consumption are considered for choosing the best network.The performance of the proposed VHO mechanism based on Fractional-DE is evaluated based on delay, energy consumption, staytime, and throughput, in which the proposed method offers the best performance.

The purpose of this paper is to focus on whether the deviations from the cointegrating relationship possess long memory and the fractional cointegration analyses may capture a wider range of mean-reversion behaviour than standard cointegration analyses.

This paper uses a fractional cointegration technique to test the purchasing power parity (PPP).

The authors found that PPP held, but very weakly, in the long run between the Argentine, Brazil, Chile, Colombia, Indonesia, Korea, Mexico, Thailand and Venezuela and US exchange rate during our floating exchange rate period but that the deviations from it did not follow a stationary process. Nevertheless, it is also found that the deviations from PPP exists and can be characterized by a fractionally integrated process in nine out of 13 countries studied.

The findings are consistent with the consensus of the empirical literature, reviewed earlier in this paper, on PPP between Argentine, Brazil, Chile, Colombia, Indonesia, Korea, Mexico, Thailand and Venezuela and the USA.

The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM).

The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator.

The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order.

To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

The purpose of this paper is to introduce a new class of fractional positive continuous‐time and discrete‐time linear systems.

Solutions to the state equations of the fractional systems are given.

Necessary and sufficient conditions are established for the internal and external positivity and of the reachability and controllability to zero of the fractional systems.

A method for analysis of the fractional positive linear systems is proposed.

Using data from 1820 onwards in a group of seven countries, namely, Australia, Chile, Denmark, France, the UK, Italy and the USA, the authors investigate if there is a long-run equilibrium relationship between the two variables (GDP and population).

Using fractional integration and cointegration methods, this paper deals with the analysis of the relationship between GDP and population using historical data.

The authors’ results show first that the two series are highly persistent, presenting orders of integration close to or above 1 in practically all cases. Testing cointegration between the two variables, the results are quite variable depending on the methodology and the bandwidth numbers used, but if cointegration takes places, it only occurs in the cases of France, Italy and the UK.

The fact that the orders of integration of all series is close to 1 indicate high levels of persistence with shocks having permanent effects and requiring strong measures to recover the original trends.

Any shock affecting the series will have a permanent nature, persisting forever.

Updated time series techniques based on concepts such as fractional integration and cointegration are used.