scholarly journals Applying fractional calculus to analyze final consumption and gross investment influence on GDP

2021 ◽  
Vol 17 (1) ◽  
pp. 65-72
Author(s):  
A. Badík ◽  
M. Fečkan
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Regression Model ◽  
Caputo Fractional Derivative ◽  
Historical Data ◽  
Model Fitting ◽  
Short Term ◽  
State Variable ◽  
Short Term Prediction ◽  
The Given

Abstract This paper points out the possibility of suitable use of Caputo fractional derivative in regression model. Fitting historical data using a regression model seems to be useful in many fields, among other things, for the short-term prediction of further developments in the state variable. Therefore, it is important to fit the historical data as accurately as possible using the given variables. Using Caputo fractional derivative, this accuracy can be increased in the model described in this paper.

Half-lives of spherical proton emitters within the framework of fractional calculus

2014 ◽  
Vol 23 (09) ◽  
pp. 1450044 ◽  
Author(s):  
Abdullah Engin Çalik ◽  
Hüseyin Şirin ◽  
Hüseyin Ertik ◽  
Buket Öder ◽  
Mürsel Şen
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Nuclear Structure ◽  
Caputo Fractional Derivative ◽  
Half Life ◽  
Nuclear Decay ◽  
Life Values ◽  
Derivative Order

In this paper, the half-life values of spherical proton emitters such as Sb , Tm , Lu , Ta , Re , Ir , Au , Tl and Bi have been calculated within the framework of fractional calculus. Nuclear decay equation, related to this phenomenon, has been resolved by using Caputo fractional derivative. The order of fractional derivative μ being considered is 0 < μ ≤ 1, and characterizes the fractality of time. Half-life values have been calculated equivalent with empirical ones. The dependence of fractional derivative order μ on the nuclear structure has also been investigated.

scholarly journals On the Existence and Uniqueness Results for Fuzzy Linear and Semilinear Fractional Evolution Equations Involving Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Existence Theorems ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction

In this manuscript, we establish new existence and uniqueness results for fuzzy linear and semilinear fractional evolution equations involving Caputo fractional derivative. The existence theorems are proved by using fuzzy fractional calculus, Picard’s iteration method, and Banach contraction principle. As application, we conclude this paper by giving an illustrative example to demonstrate the applicability of the obtained results.

scholarly journals Modeling the Dynamics and Forecasting the fourth Peak of COVID-19 in Iran Using PSO Algorithm

2021 ◽  
Vol 8 (4) ◽  
pp. 140-145
Author(s):  
Ebrahim Sahafizadeh ◽  
Mohammad Ali Khajeian
Keyword(s):  
Pso Algorithm ◽  
Future Trend ◽  
Short Term ◽  
Estimated Parameters ◽  
Term Prediction ◽  
Proposed Model ◽  
Spread Model ◽  
Short Term Prediction ◽  
Reported Data ◽  
The Given

Background and aims: Iran had passed the third peak of COVID-19 pandemic, and was probably witnessing the fourth peak at the time of this study. This study aimed to model the spread of COVID-19 in Iran in order to predict the short-term future trend of COVID-19 from April 23, 2021 to May 7, 2021. Methods: In this study, a modified SEIR epidemic spread model was proposed and the data on the number of cases reported by Iranian government from February 20, 2020 to April 23, 2021 were used to fit the proposed model to the reported data using particle swarm optimization (PSO) algorithm. Then the short-term future trend of COVID-19 cases were predicted by using the estimated parameters. Results: The results indicated that the effective reproduction number increased in Nowruz (i.e., Persian New Year, 1400) and it was estimated to be 1.28 in the given period. According to the results from the short-term prediction of COVID-19 cases, the number of active confirmed cases in the fourth peak was estimated to be 516411 cases on May 2, 2021. Conclusion: Following the results from our short-term prediction, implementing strict social distancing policies was found absolutely necessary for relieving the Iran’s health care system of the tremendous burden of COVID-19.

Initialization Issues of the Caputo Fractional Derivative

2005 ◽  
Author(s):  
B. N. Narahari Achar ◽  
Carl F. Lorenzo ◽  
Tom T. Hartley
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Past History ◽  
The Past ◽  
History Of ◽  
Fractional Differential ◽  
Generally True

The importance of proper initialization in taking into account the history of a system whose time evolution is governed by a differential equation of fractional order, has been established by Lorenzo and Hartley, who also gave the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann-Liouville and the Grunwald formulations of fractional calculus. The present work addresses this issue for the Caputo fractional derivative and cautions that the commonly held belief that the Caputo formulation of fractional derivatives properly accounts for the initialization effects is not generally true when applied to the solution of fractional differential equations.

scholarly journals Solution of Fractional Order Equations in the Domain of the Mellin Transform

2019 ◽  
pp. 138-142
Author(s):  
Sunday Emmanuel Fadugba
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Mellin Transform ◽  
Applied Mathematics ◽  
Fundamental Properties ◽  
Sequential Fractional Derivative ◽  
Liouville Fractional Derivative

This paper presents the Mellin transform for the solution of the fractional order equations. The Mellin transform approach occurs in many areas of applied mathematics and technology. The Mellin transform of fractional calculus of different flavours; namely the Riemann-Liouville fractional derivative, Riemann-Liouville fractional integral, Caputo fractional derivative and the Miller-Ross sequential fractional derivative were obtained. Three illustrative examples were considered to discuss the applications of the Mellin transform and its fundamental properties. The results show that the Mellin transform is a good analytical method for the solution of fractional order equations.

scholarly journals On the Stability of Fractional Differential Equations Involving Generalized Caputo Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Minh Duc Tran ◽  
Vu Ho ◽  
Hoa Ngo Van
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Caputo Derivative ◽  
Fractional Differential ◽  
The Stability ◽  
The Given

This work presents the results of the global existence for fractional differential equations involving generalized Caputo derivative with the case of the fractional order derivative α∈1,2. In addition, the Ulam–Hyers–Mittag-Leffler stability of the given problems is also established.

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