Journal Article10.1016/J.CHAOS.2019.06.011
Crank-Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana-Baleanu Caputo derivative
Ali Akgül,Mahmut Modanli +1 more
58
TL;DR: In this article, the third order partial differential equation defined by Caputo fractional derivative with Atangana-Baleanu derivative has been investigated and the stability estimates are proved for the exact solution.
read more
Abstract: In this paper, the third order partial differential equation defined by Caputo fractional derivative with Atangana–Baleanu derivative has been investigated. The stability estimates are proved for the exact solution. Difference schemes for Crank–Nicholson finite difference scheme method is constructed. The stability of difference schemes for this problem is shown by Von Neumann method (Fourier analysis method). Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the technique. The reproducing kernel function for the problem has been found.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative
TL;DR: In this paper, a numerical approach to the immunogenetic tumour model using differential and integral operators with Mittag-Leffler law was made, where fractional Atangana- Baleanu derivative has been utilized in the structure of proposed model.
335
A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials
TL;DR: The behaviors of susceptible, exposed, infected, and recovered individuals are presented graphically at the value of various fractional order and the solutions with Adams‐Bashforth‐Moulton predictor corrector scheme for the accuracy and applicability of the Genocchi wavelets method (GWM).
194
A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment
Sunil Kumar,Ajay Kumar,Bessem Samet,José Francisco Gómez-Aguilar,Mohamed S. Osman,Mohamed S. Osman +5 more
TL;DR: This paper analyses the existence and uniqueness of given tumor-immune model of arbitrary order, and examines the interactions among distinct tumor cell inhabitants and immune structure through a model of real world problem of medical science.
184
A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing
TL;DR: The obtained experimental results show that the proposed fractional masks are computationally efficient, and their performances are compatible with other standard and fractional smoothing filters.
176
References
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
Abdon Atangana,Dumitru Baleanu +1 more
TL;DR: In this article, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.
•Posted Content
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
Abdon Atangana,Dumitru Baleanu +1 more
TL;DR: In this paper, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.
1.3K
Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order
Abdon Atangana,Ilknur Koca +1 more
TL;DR: In this paper, Atangana and Baleanu proposed a derivative with fractional order to answer some outstanding questions that were posed by many researchers within the field of fractional calculus.
812
Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
Cem Çelik,Melda Duman +1 more
TL;DR: The Crank-Nicolson method is applied to a fractional diffusion equation which has the Riesz fractional derivative, and it is obtained that the method is unconditionally stable and convergent.
496
New numerical approach for fractional differential equations
Abdon Atangana,Kolade M. Owolabi +1 more
TL;DR: In this paper, the authors proposed the correct fractional Adams-Bashforth method which takes into account the nonlinearity of the kernels including the power law for Riemann-Liouville type, the exponential decay law for the Caputo-Fabrizio case and the Mittag-Leffler law for Atangana-Baleanu scenario.
277