scholarly journals Numerical Computation of a Fractional Derivative with Non-Local and Non-Singular Kernel

2017 ◽  
Vol 12 (3) ◽  
pp. 4-13 ◽  
Author(s):  
J.D. Djida ◽  
A. Atangana ◽  
I. Area
Keyword(s):  
Fractional Derivative ◽  
Numerical Computation ◽  
Singular Kernel ◽  
Non Local

A novel method for a fractional derivative with non-local and non-singular kernel

2018 ◽  
Vol 114 ◽  
pp. 478-482 ◽  
Author(s):  
Ali Akgül
Keyword(s):  
Fractional Derivative ◽  
Singular Kernel ◽  
Novel Method ◽  
Non Local

scholarly journals Modified Kawahara equation within a fractional derivative with non-singular kernel

2018 ◽  
Vol 22 (2) ◽  
pp. 789-796 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Numerical Solution ◽  
Water Waves ◽  
Iterative Scheme ◽  
Singular Kernel ◽  
Kawahara Equation ◽  
Long Wavelength ◽  
Exponential Kernel ◽  
The Stability ◽  
Linear Water Waves

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

scholarly journals Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Mostafa Tahiri ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Optimality Conditions ◽  
Fractional Derivatives ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Derivative Operator ◽  
Sir Epidemic ◽  
Non Local

<p style='text-indent:20px;'>The main aim of the present work is to study and analyze a reaction-diffusion fractional version of the SIR epidemic mathematical model by means of the non-local and non-singular ABC fractional derivative operator with complete memory effects. Existence and uniqueness of solution for the proposed fractional model is proved. Existence of an optimal control is also established. Then, necessary optimality conditions are derived. As a consequence, a characterization of the optimal control is given. Lastly, numerical results are given with the aim to show the effectiveness of the proposed control strategy, which provides significant results using the AB fractional derivative operator in the Caputo sense, comparing it with the classical integer one. The results show the importance of choosing very well the fractional characterization of the order of the operators.</p>

scholarly journals On fractional modelling of dye removal using fractional derivative with non-singular kernel

2019 ◽  
Vol 31 (4) ◽  
pp. 525-527 ◽  
Author(s):  
Norodin A. Rangaig ◽  
Vernie C. Convicto
Keyword(s):  
Fractional Derivative ◽  
Dye Removal ◽  
Singular Kernel

Conservatory of Kaup-Kupershmidt Equation to the Concept of Fractional Derivative with and without Singular Kernel

2018 ◽  
Vol 34 (2) ◽  
pp. 351-361 ◽  
Author(s):  
Abdon Atangana ◽  
Emile Franc Doungmo Goufo
Keyword(s):  
Fractional Derivative ◽  
Singular Kernel
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