scholarly journals Fractional virus epidemic model on financial networks

2016 ◽  
Vol 14 (1) ◽  
pp. 1074-1086 ◽  
Author(s):  
Mehmet Ali Balci
Keyword(s):  
Time Series ◽  
Epidemic Model ◽  
Stock Markets ◽  
Global Memory ◽  
Transform Method ◽  
Data Set ◽  
Theoretical Concepts ◽  
Differential Transform ◽  
Long Time ◽  
Fractional Differential

AbstractIn this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

scholarly journals Solution of HIV and Malaria Coinfection Model Using Msgdtm

2015 ◽  
Vol 7 (4) ◽  
pp. 181
Author(s):  
Bonyah Ebenezer ◽  
Kwasi Awuah-Werekoh ◽  
Joseph Acquah
Keyword(s):  
Approximate Solution ◽  
Fractional Order ◽  
Epidemic Model ◽  
Unique Positive Solution ◽  
Transform Method ◽  
Order Form ◽  
Differential Transform ◽  
Infection Disease ◽  
Generalized Differential ◽  
Order Four

<p>In this paper, we investigate an epidemic model of HIV and Malaria co-infection using fractional order Calculus (FOC). The multistep generalized differential transform method (MSGDTM) is employed to obtain an accurate approximate solution to the epidemic model of HIV and Malaria co-infection disease in fractional order. A unique positive solution for HIV and Malaria co-infection is presented in fractional order form. For the integer case derivatives, the approximate solution of MSGDTM and the Runge–Kutta–order four scheme are compared. Numerical results are produced for the justification for this method.</p>

Analysing “Long Data” on Collective Violence in Indonesia

2015 ◽  
Vol 43 (5) ◽  
pp. 613-633
Author(s):  
David A. Meyer ◽  
Arthur Stein
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Model Building ◽  
Collective Violence ◽  
Temporal Data ◽  
Data Set ◽  
Time Correlations ◽  
Long Time ◽  
Short Time ◽  
Periodic Components

“Long data”, i.e., temporal data disaggregated to short time intervals to form a long time series, is a particularly interesting type of “big data”. Financial data are often available in this form (e.g., many years of daily stock prices), but until recently long data for other social, and even other economic, processes have been rare. Over the last decade, however, long data have begun to be extracted from (digitized) text, and then used to assess or formulate micro-level and macro-level theories. The UN Support Facility for Indonesian Recovery (UNSFIR) collected a long data set of incidents of collective violence in 14 Indonesian provinces during the 14 year period 1990–2003. In this paper we exploit the “length” of the UNSFIR data by applying several time series analysis methods. These reveal some previously unobserved features of collective violence in Indonesia—including periodic components and long time correlations—with important social/political interpretations and consequences for explanatory model building.

scholarly journals Solving time-fractional chemical engineering equations by generalized differential transform method

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 157-164
Author(s):  
Ahmad Haghbin ◽  
Hossein Jafari ◽  
Pranay Goswami ◽  
Morganathan Ariyan
Keyword(s):  
Chemical Reaction ◽  
Chemical Engineering ◽  
Convergent Series ◽  
High Accuracy ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Generalized Differential

In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient.

scholarly journals Solving time-fractional chemical engineering equations by generalized differential transform method

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 157-164
Author(s):  
Ahmad Haghbin ◽  
Hossein Jafari ◽  
Pranay Goswami ◽  
Morganathan Ariyan
Keyword(s):  
Chemical Reaction ◽  
Chemical Engineering ◽  
Convergent Series ◽  
High Accuracy ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Generalized Differential

In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient.

New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Feras Yousef ◽  
Marwan Alquran ◽  
Imad Jaradat ◽  
Shaher Momani ◽  
Dumitru Baleanu
Keyword(s):  
Analytical Study ◽  
Three Dimensional ◽  
Fractional Power ◽  
Differential Transform Method ◽  
Initial Value ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Models ◽  
Fractional Differential ◽  
Fractional Power Series

Abstract Herein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a γ¯-fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.

Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order

2021 ◽  
Vol 8 (3) ◽  
pp. 537-548
Author(s):  
S. E. Fadugba ◽  
◽  
F. Ali ◽  
A. B. Abubakar ◽  
◽  
...  
Keyword(s):  
Power Series ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Epidemic Model ◽  
Differential Transform Method ◽  
Host Community ◽  
Convergent Power Series ◽  
Transform Method ◽  
Differential Transform ◽  
Reduced Differential Transform Method

This paper proposes the Caputo Fractional Reduced Differential Transform Method (CFRDTM) for Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model with fractional order in a host community. CFRDTM is the combination of the Caputo Fractional Derivative (CFD) and the well-known Reduced Differential Transform Method (RDTM). CFRDTM demonstrates feasible progress and efficiency of operation. The properties of the model were analyzed and investigated. The fractional SEIR epidemic model has been solved via CFRDTM successfully. Hence, CFRDTM provides the solutions of the model in the form of a convergent power series with easily computable components without any restrictive assumptions.

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