scholarly journals About the convergence type of improper integrals defining fractional derivatives

2019 ◽  
Vol 23 (1) ◽  
pp. 95-102
Author(s):  
B. Kalam ◽  
G. Vainikko
Keyword(s):  
Pointwise Convergence ◽  
Fractional Derivatives ◽  
Absolute Convergence ◽  
Conditional Convergence ◽  
Differentiable Functions ◽  
Improper Integrals ◽  
Convergence Type

This article continues the analysis of the class of fractionally differentiable functions. We complete the main result of [4] that characterises the class of fractionally differentiable functions in terms of the pointwise convergence of certain improper integrals containing these functions. Our aim is to present an example, which shows that in order to obtain all fractionally differentiable functions, one may not replace the conditional convergence of those integrals by their absolute convergence.

scholarly journals The Analysis of Income per Capita Convergence on ASEAN Plus Three (APT) Countries

2017 ◽  
Vol 1 (1) ◽  
pp. 51
Author(s):  
Any Fatiwetunusa ◽  
Syamsurijal Syamsurijal ◽  
Sa’adah Yuliana
Keyword(s):  
Absolute Convergence ◽  
Value Added ◽  
Gdp Per Capita ◽  
Conditional Convergence ◽  
Income Per Capita ◽  
Real Gdp ◽  
Real Gdp Per Capita ◽  
Per Capita ◽  
Convergence Model ◽  
The Impact

The main objective of this study is to test the convergence of income per capita in APT countries through three models: absolute convergence, conditional convergence and sigma convergence. Regression analysis of panel data from 13 APT countries during the period of 2001-2014 is used to analysed to study problem. In absolute convergence model, the growth of real GDP per capita and initial real GDP are used as the variables, meanwhile, 8 variables such as the growth of real GPD per capita, initial real GDP per capita, labor force ratio, value added in agricultural sector, value added in industrial sector, terms of trade, foreign direct investment and internet users ratio are analyzed in conditional convergence model. According to the Solow model, the economies of the countries will converge in which the growth of income per capita of developing countries will be higher than those of developed countries. The economies will be convergent if the countries tend to move to a similar steady state resulting in smaller gap between the countries. Based on the results of absolute convergence and conditional convergence models, APT countries is converging with the rate of 2% and 2.2%. This is consistent with the results of sigma convergence model that shows a declining trend in the dispersion of real GDP per capita in APT regions. The growth of real GDP per capita is influenced by initial GDP per capita, labor force ratio, value added in agricultural sector, value added in industrial sector, terms of trade, foreign direct investment and internet users ratio. Developed countries such as Singapore, Brunei Darussalam and South Korea experience the impact of high real GDP per capita growth. On the contrary, Indonesia, Laos, Vietnam and The Phillipines undergo the impact of low GDP per capita growth.

Lagrangian Formulation of Lorenz and Chen Systems

2021 ◽  
Vol 31 (04) ◽  
pp. 2150055
Author(s):  
Palanisamy Vijayalakshmi ◽  
Zhiheng Jiang ◽  
Xiong Wang
Keyword(s):  
Fractional Derivatives ◽  
Lagrangian Function ◽  
Conserved Quantity ◽  
Lagrangian Formulation ◽  
Lagrangian Functions ◽  
Differentiable Functions ◽  
Derivatives Of

This paper presents the formulation of Lagrangian function for Lorenz, Modified Lorenz and Chen systems using Lagrangian functions depending on fractional derivatives of differentiable functions, and the estimation of the conserved quantity associated with the respective systems.

scholarly journals Fractional Variational Problems Depending on Fractional Derivatives of Differentiable Functions with Application to Nonlinear Chaotic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Matheus Jatkoske Lazo
Keyword(s):  
Dynamical Systems ◽  
Fractional Derivatives ◽  
Chaotic Systems ◽  
Lagrange Equation ◽  
Variational Problems ◽  
Necessary Condition ◽  
Chaotic Dynamical Systems ◽  
Differentiable Functions ◽  
Fractional Variational Problems ◽  
Derivatives Of

We formulate a necessary condition for functionals with Lagrangians depending on fractional derivatives of differentiable functions to possess an extremum. The Euler-Lagrange equation we obtained generalizes previously known results in the literature and enables us to construct simple Lagrangians for nonlinear systems. As examples of application, we obtain Lagrangians for some chaotic dynamical systems.

scholarly journals On Hadamard-type inequalities for differentiable functions via Caputo k-fractional derivatives

2017 ◽  
Vol 4 (1) ◽  
pp. 1355429 ◽  
Author(s):  
Ghulam Farid ◽  
Anum Javed ◽  
Atiq ur Rehman ◽  
Muhammad Imran Qureshi ◽  
Lishan Liu
Keyword(s):  
Fractional Derivatives ◽  
Differentiable Functions

scholarly journals Estimates of Mean-Type Fractional Inequalities For Differentiable Functions

2021 ◽  
Author(s):  
Muhammad Samraiz ◽  
Zahida Perveen ◽  
Sajid Iqbal ◽  
Saima Naheed ◽  
Thabet Abdeljawad
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Hilfer Fractional Derivative ◽  
Caputo Fractional Derivatives ◽  
Differentiable Functions ◽  
Wide Range ◽  
Type Integral ◽  
Special Case

In this article, we established a wide range of fractional mean-type integral inequalities for notable Hilfer fractional derivative using twice differentiable convex and $s$-convex functions for $s\in(0,1]$ with related identities. Also the results for Caputo fractional derivatives are derived as a special case of our general results.

scholarly journals Dampak Desentralisasi Fiskal terhadap Konvergensi Pendapatan Perkapita antar Kabupaten/Kota di Indonesia

2021 ◽  
Vol 6 (1) ◽  
pp. 1-18
Author(s):  
Bonnie Permana Negara ◽  
Khoirunurrofik Khoirunurrofik
Keyword(s):  
Absolute Convergence ◽  
Conditional Convergence

Dengan menggunakan data panel 505 kabupaten/kota di Indonesia selama periode pelaksanaan desentralisasi dari tahun 2001-2017, penelitian ini bertujuan untuk menguji tentang indikasi konvergensi perekonomian antar daerah di Indonesia dan untuk mengetahui pengaruh kebijakan desentralisasi fiskal terhadap konvergensi pendapatan perkapita antar daerah di Indonesia. Indikator desentralisasi fiskal menggunakan indikator pendapatan dan indikator belanja daerah. Indikator pendapatan daerah terdiri dari pendapatatan asli daerah, dana bagi hasil, dan dana transfer. Indikator belanja daerah fokus pada belanja sektor pendidikan, sektor kesehatan, dan sektor infrastruktur. Menggunakan analisa konvergensi statis, penelitian ini menemukan bukti bahwa terjadi konvergensi pendapatan perkapita antar kabupaten/kota di Indonesia. Analisa konvergensi dinamis dengan model absolute convergence dan conditional convergence. Hasil estimasi model absolute convergence menunjukkan terjadinya konvergensi pendapatan perkapita antar kabupaten/kota di Indonesia dengan tingkat konvergensi sebesar 7 persen. Sedangkan hasil estimasi model conditional convergence menghasilkan tingkat konvergensi sebesar 19 persen ketika tenaga kerja, investasi, angka partisipasi pendidikan, dan indikator desentralisasi fiskal disertakan dalam model.

scholarly journals The Analysis of Income per Capita Convergence on ASEAN Plus Three (APT) Countries

2017 ◽  
Vol 1 (1) ◽  
pp. 51
Author(s):  
Any Fatiwetunusa ◽  
Syamsurijal Syamsurijal ◽  
Sa’adah Yuliana
Keyword(s):  
Absolute Convergence ◽  
Value Added ◽  
Gdp Per Capita ◽  
Conditional Convergence ◽  
Income Per Capita ◽  
Real Gdp ◽  
Real Gdp Per Capita ◽  
Per Capita ◽  
Convergence Model ◽  
The Impact

The main objective of this study is to test the convergence of income per capita in APT countries through three models: absolute convergence, conditional convergence and sigma convergence. Regression analysis of panel data from 13 APT countries during the period of 2001-2014 is used to analysed to study problem. In absolute convergence model, the growth of real GDP per capita and initial real GDP are used as the variables, meanwhile, 8 variables such as the growth of real GPD per capita, initial real GDP per capita, labor force ratio, value added in agricultural sector, value added in industrial sector, terms of trade, foreign direct investment and internet users ratio are analyzed in conditional convergence model. According to the Solow model, the economies of the countries will converge in which the growth of income per capita of developing countries will be higher than those of developed countries. The economies will be convergent if the countries tend to move to a similar steady state resulting in smaller gap between the countries. Based on the results of absolute convergence and conditional convergence models, APT countries is converging with the rate of 2% and 2.2%. This is consistent with the results of sigma convergence model that shows a declining trend in the dispersion of real GDP per capita in APT regions. The growth of real GDP per capita is influenced by initial GDP per capita, labor force ratio, value added in agricultural sector, value added in industrial sector, terms of trade, foreign direct investment and internet users ratio. Developed countries such as Singapore, Brunei Darussalam and South Korea experience the impact of high real GDP per capita growth. On the contrary, Indonesia, Laos, Vietnam and The Phillipines undergo the impact of low GDP per capita growth.

Sign in / Sign up

Export Citation Format

Share Document