scholarly journals The Leibniz Rule for Fractional Derivatives Holds with Non-Differentiable Functions

2013 ◽  
Vol 1 (2) ◽  
pp. 50-52
Author(s):  
Guy Jumarie
Keyword(s):  
Fractional Derivatives ◽  
Leibniz Rule ◽  
Differentiable Functions

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 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 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
Sign in / Sign up

Export Citation Format

Share Document