On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions

2020 ◽  
Vol 139 ◽  
pp. 110012 ◽  
Author(s):  
C. Ravichandran ◽  
K. Logeswari ◽  
Sumati Kumari Panda ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fractional Derivative ◽  
Differential Systems ◽  
Impulsive Conditions ◽  
New Approach

scholarly journals Modeling the potential energy field caused by mass density distribution with Eton approach

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 106-113 ◽  
Author(s):  
Badr Saad T. Alkahtani ◽  
Abdon Atangana
Keyword(s):  
Potential Energy ◽  
Fractional Derivative ◽  
Mass Density ◽  
Variable Order ◽  
Modified Model ◽  
New Approach ◽  
Energy Field ◽  
Variable Order Derivative ◽  
With Memory ◽  
Real World Problems

AbstractA new approach for modeling real world problems called the “Eton Approach” was presented in this paper. The "Eton approach" combines both the concept of the variable order derivative together with Atangana derivative with memory derivative. The Atangana derivative with memory is used to account for the memory and fractional derivative for its filter effect. The approach was used to describe the potential energy field that is caused by a given charge or mass density distribution.We solve the modified model numerically and present supporting numerical simulations.

scholarly journals Modeling and Application of a New Nonlinear Fractional Financial Model

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yiding Yue ◽  
Lei He ◽  
Guanchun Liu
Keyword(s):  
Interest Rate ◽  
Fractional Derivative ◽  
Empirical Model ◽  
Econometric Model ◽  
System Modeling ◽  
Financial System ◽  
Actual Data ◽  
Time Step ◽  
Financial Model ◽  
New Approach

The paper proposes a new nonlinear dynamic econometric model with fractional derivative. The fractional derivative is defined in the Jumarie type. The corresponding discrete financial system is considered by removing the limit operation in Jumarie derivative’s. We estimate the coefficients and parameters of the model by using the least squared principle. The new approach to financial system modeling is illustrated by an application to model the behavior of Japanese national financial system which consists of interest rate, investment, and inflation. The empirical results with different time step sizes of discretization are shown, and a comparison of the actual data against the data estimated by empirical model is illustrated. We find that our discrete financial model can describe the actual data that include interest rate, investment, and inflation accurately.

scholarly journals New approach to the fractional derivatives

2003 ◽  
Vol 2003 (5) ◽  
pp. 315-325 ◽  
Author(s):  
Kostadin Trenčevski
Keyword(s):  
Positive Integer ◽  
Fractional Derivative ◽  
Taylor Expansion ◽  
Fractional Derivatives ◽  
Analytical Continuation ◽  
New Approach ◽  
Analytical Functions ◽  
Summation Of Divergent Series ◽  
Summation Of Series ◽  
Derivatives Of

We introduce a new approach to the fractional derivatives of the analytical functions using the Taylor series of the functions. In order to calculate the fractional derivatives off, it is not sufficient to know the Taylor expansion off, but we should also know the constants of all consecutive integrations off. For example, any fractional derivative ofexisexonly if we assume that thenth consecutive integral ofexisexfor each positive integern. The method of calculating the fractional derivatives very often requires a summation of divergent series, and thus, in this note, we first introduce a method of such summation of series via analytical continuation of functions.

scholarly journals Analytic Approach for Solving System of Fractional Differential Equations

2021 ◽  
Vol 32 (1) ◽  
pp. 14
Author(s):  
Nabaa N Hasan ◽  
Zainab John
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Initial Conditions ◽  
Analytic Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

In this paper, Sumudu transformation (ST) of Caputo fractional derivative formulae are derived for linear fractional differential systems. This formula is applied with Mittage-Leffler function for certain homogenous and nonhomogenous fractional differential systems with nonzero initial conditions. Stability is discussed by means of the system's distinctive equation.

scholarly journals On linear and nonlinear fractional PDEs

2013 ◽  
Vol 40 (4) ◽  
pp. 511-524
Author(s):  
Jamshad Ahmad ◽  
Hassany ul ◽  
Syed Mohyud-Din
Keyword(s):  
Exact Solution ◽  
Fractional Derivative ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Nonlinear Partial Differential Equations ◽  
Variational Iteration Method ◽  
High Accuracy ◽  
New Approach ◽  
Fractional Pdes ◽  
Linear And Nonlinear

In this study, Variational Iteration Method (VIM) has been applied to obtain the analytical solutions of fractional order nonlinear partial differential equations. The iteration procedure is based on a relatively new approach which is called Jumarie?s fractional derivative. Several examples have been solved to elucidate effectiveness of the proposed method and the results are compared with the exact solution, revealing high accuracy and efficiency of the method.

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