Atangana-Batogna numerical scheme applied on a linear and non-linear fractional differential equation

2018 ◽  
Vol 133 (3) ◽  
Author(s):  
Badr Saad T. Alkahtani
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Numerical Scheme ◽  
Non Linear ◽  
Fractional Differential

scholarly journals Ulam-Hyers Stability for Cauchy Fractional Differential Equation in the Unit Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Unit Disk ◽  
Fractional Differential Equations ◽  
Fractional Operators ◽  
Owa Operators ◽  
Non Linear ◽  
Fractional Differential

We prove the Ulam-Hyers stability of Cauchy fractional differential equations in the unit disk for the linear and non-linear cases. The fractional operators are taken in sense of Srivastava-Owa operators.

scholarly journals Numerical Approximation of Riccati Fractional Differential Equation in the Sense of Caputo-Type Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xin Liu ◽  
Kamran ◽  
Yukun Yao
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Numerical Scheme ◽  
Robust Stabilization ◽  
Smooth Curve ◽  
Quadrature Rule ◽  
Network Synthesis ◽  
Riccati Differential Equation ◽  
Bromwich Integral ◽  
Fractional Differential

The Riccati differential equation is a well-known nonlinear differential equation and has different applications in engineering and science domains, such as robust stabilization, stochastic realization theory, network synthesis, and optimal control, and in financial mathematics. In this study, we aim to approximate the solution of a fractional Riccati equation of order 0<β<1 with Atangana–Baleanu derivative (ABC). Our numerical scheme is based on Laplace transform (LT) and quadrature rule. We apply LT to the given fractional differential equation, which reduces it to an algebraic equation. The reduced equation is solved for the unknown in LT space. The solution of the original problem is retrieved by representing it as a Bromwich integral in the complex plane along a smooth curve. The Bromwich integral is approximated using the trapezoidal rule. Some numerical experiments are performed to validate our numerical scheme.

Simple Identification of Fractional Differential Equation

2011 ◽  
Vol 180 ◽  
pp. 331-338 ◽  
Author(s):  
Wojciech Mitkowski ◽  
Anna Obrączka
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Numerical Experiments ◽  
Identification Problem ◽  
Marquardt Algorithm ◽  
Non Linear ◽  
Fractional Differential ◽  
Estimation Parameters

In this paper the simple identification problem for fractional differential equation of Caputo type was considered. This is the problem of estimation parameters, for which the quadratic criterion is minimized. For solving this issue, the Non Linear Programing technique, based on Marquardt algorithm, was used. At the end of article the results for numerical experiments was presented.

scholarly journals The generalized Gegenbauer-Humberts wavelet for solving fractional differential equations

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 107-118
Author(s):  
Jumana Alkhalissi ◽  
Ibrahim Emiroglu ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
New Method ◽  
Algebraic Equations ◽  
Non Linear ◽  
Fractional Differential ◽  
Operational Matrix Of Integration

In this paper we present a new method of wavelets, based on generalized Gegen?bauer-Humberts polynomials, named generalized Gegenbauer-Humberts wave?lets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.

scholarly journals The generalized Gegenbauer-Humberts wavelet for solving fractional differential equations

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 107-118
Author(s):  
Jumana Alkhalissi ◽  
Ibrahim Emiroglu ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
New Method ◽  
Algebraic Equations ◽  
Non Linear ◽  
Fractional Differential ◽  
Operational Matrix Of Integration

In this paper we present a new method of wavelets, based on generalized Gegen?bauer-Humberts polynomials, named generalized Gegenbauer-Humberts wave?lets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.

scholarly journals Solution of Multi-order Fractional Differential Equation Based on Conformable Derivative by Shifted Legendre Polynomial

2021 ◽  
Vol 5 (2) ◽  
pp. 64-68
Author(s):  
Salim S. Mahmood ◽  
Kamaran J. Hamad ◽  
‎Milad A. Kareem ◽  
Asrin F. Shex
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear Equation ◽  
Fractional Differential Equation ◽  
Legendre Polynomial ◽  
Conformable Derivative ◽  
Approximation Solution ◽  
Non Linear Equation ◽  
Non Linear ◽  
Fractional Differential

The aim of this article is the way for finding approximation solution of multi-order fractional differential equation with conformable sense with use approximated function by shifted Legendre polynomial, the method is easy and powerful for get our results of the linear and non-linear equation, the background idea behind this method is finding system of algebra after achieving messing variable is that mean obtain approximate solution, a few examples illustrates for presented how much our method is capable.

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