Journal ArticleDOI
New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models
Mekkaoui Toufik,Abdon Atangana +1 more
TLDR
In this paper, a new numerical scheme has been developed for the newly established fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives.Abstract:
Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.read more
Citations
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Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative
TL;DR: In this paper, the authors describe the mathematical modeling and dynamics of a novel corona virus (2019-nCoV) and present the mathematical results of the model and then formulate a fractional model.
Journal ArticleDOI
Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties
TL;DR: In this paper, an analysis of evolutions equations generated by three fractional derivatives namely the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives is presented.
Journal ArticleDOI
Fractional derivatives with no-index law property: Application to chaos and statistics
TL;DR: In this article, the authors showed that fractional operators obeying index law cannot model real world problems taking place in two states, more precisely they cannot describe phenomena taking place beyond their boundaries, as they are scaling invariant, more specifically their results show that, mathematical models based on these differential operators are not able to describe the inverse memory, meaning the full history of a physical problem cannot be described accurately using these derivatives with index law properties.
Journal ArticleDOI
On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative
TL;DR: In this paper, the conditions of existence and uniqueness of solutions to a certain class of ordinary differential equations involving Atangana-Baleanu fractional derivative were discussed. And the stability of such equations in the sense of Ulam was studied.
Journal ArticleDOI
Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan
TL;DR: A fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana–Baleanu–Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed and the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals.
References
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Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Book
Solving Ordinary Differential Equations I: Nonstiff Problems
TL;DR: In this paper, the authors describe the historical development of the classical theory of linear methods for solving nonstiff ODEs and present a modern treatment of Runge-Kutta and extrapolation methods.
Journal ArticleDOI
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.
Book
Numerical Methods for Ordinary Differential Systems: The Initial Value Problem
TL;DR: In this paper, the authors introduce numerical methods for nonlinear stability theory and linear multi-step methods for linear stability theory, including Predictor-Corrector Methods and Runge-Kutta Methods.
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New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
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