Chaos in a 5-D hyperchaotic system with four wings in the light of non-local and non-singular fractional derivatives

2018 ◽  
Vol 116 ◽  
pp. 316-331 ◽  
Author(s):  
Ebenezer Bonyah
Keyword(s):  
Fractional Derivatives ◽  
Hyperchaotic System ◽  
Non Local

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 Non-local fractional derivatives. Discrete and continuous

2017 ◽  
Vol 449 (1) ◽  
pp. 734-755 ◽  
Author(s):  
Luciano Abadias ◽  
Marta De León-Contreras ◽  
José L. Torrea
Keyword(s):  
Fractional Derivatives ◽  
Non Local

ANALYTIC CONTINUATION OF OPERATORS APPLICATIONS: FROM NUMBER THEORY AND GROUP THEORY TO QUANTUM FIELD AND STRING THEORIES

1999 ◽  
Vol 11 (04) ◽  
pp. 463-501 ◽  
Author(s):  
S. C. WOON
Keyword(s):  
Number Theory ◽  
Analytic Continuation ◽  
Particle Physics ◽  
Fractional Derivatives ◽  
Bernoulli Polynomials ◽  
Local Effect ◽  
Quantum Field ◽  
Matrix Representations ◽  
Complex Power ◽  
Non Local

We are used to thinking of an operator acting once, twice, and so on. However, an operator can be analytically continued to the operator raised to a complex power. Applications include (s,r) diagrams and an extension of Fractional Calculus where commutativity of fractional derivatives is preserved, generating integrals and non-standard derivations of theorems in Number Theory, non-integer power series and breaking of Leibniz and Chain rules, pseudo-groups and symmetry deforming models in particle physics and cosmology, non-local effect in analytically continued matrix representations and its connection with noncommutative geometry, particle-physics-like scatterings of zeros of analytically continued Bernoulli polynomials, and analytic continuation of operators in QM, QFT and Strings.

scholarly journals Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 675
Author(s):  
Rubayyi T. Alqahtani ◽  
Abdullahi Yusuf ◽  
Ravi P. Agarwal
Keyword(s):  
Fractional Derivatives ◽  
Oxygen Uptake Rate ◽  
Continuous Process ◽  
Equilibrium Stability ◽  
Treatment Model ◽  
Classical Version ◽  
Fractional Differential Operator ◽  
Non Local ◽  
Fractional Differential ◽  
Steady State Solutions

In this paper, the wastewater treatment model is investigated by means of one of the most robust fractional derivatives, namely, the Caputo fractional derivative. The growth rate is assumed to obey the Contois model, which is often used to model the growth of biomass in wastewaters. The characteristics of the model under consideration are derived and evaluated, such as equilibrium, stability analysis, and steady-state solutions. Further, important characteristics of the fractional wastewater model allow us to understand the dynamics of the model in detail. To this end, we discuss several important analyses of the fractional variant of the model under consideration. To observe the efficiency of the non-local fractional differential operator of Caputo over its counter-classical version, we perform numerical simulations.

scholarly journals Conformable heat equation on a radial symmetric plate

2017 ◽  
Vol 21 (2) ◽  
pp. 819-826 ◽  
Author(s):  
Derya Avci ◽  
Eroglu Iskender ◽  
Necati Ozdemir
Keyword(s):  
Fundamental Solution ◽  
Heat Equation ◽  
Analytical Method ◽  
Numerical Scheme ◽  
Fractional Derivatives ◽  
Problem Formulation ◽  
Computational Results ◽  
Conformable Derivative ◽  
Local Structures ◽  
Non Local

The conformable heat equation is defined in terms of a local and limit-based definition called conformable derivative which provides some basic properties of integer order derivative such that conventional fractional derivatives lose some of them due to their non-local structures. In this paper, we aim to find the fundamental solution of a conformable heat equation acting on a radial symmetric plate. Moreover, we give a comparison between the new conformable and the existing Grunwald-Letnikov solutions of heat equation. The computational results show that conformable formulation is quite successful to show the sub-behaviors of heat process. In addition, conformable solution can be obtained by a analytical method without the need of a numerical scheme and any restrictions on the problem formulation. This is surely a significant advantageous compared to the Grunwald-Letnikov solution.

Singular and Non-Singular Kernels Aspect of Time-Fractional Coupled Spring-Mass System

2021 ◽  
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty
Keyword(s):  
Fractional Derivatives ◽  
Polynomial Interpolation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Mass System ◽  
Dynamical Behaviors ◽  
Uniqueness Of The Solution ◽  
Singular Kernels ◽  
Local Operators ◽  
Non Local

Abstract Dynamical behaviors of the time-fractional nonlinear model of the coupled spring-mass system with damping have been explored here. Fractional derivatives with singular and non-singular kernels are used to assess the suggested model. The fractional Adams-Bashforth numerical method based on Lagrange polynomial interpolation is applied to solve the system with non-local operators. Existence, Ulam-Hyers stability, and uniqueness of the solution are established by using fixed-point theory and nonlinear analysis. Further, the error analysis of the present method has also been included. Finally, the behavior of the solution is explained by graphical representations through numerical simulations.

scholarly journals Solutions of Cattaneo-Hristov model of elastic heat diffusion with Caputo-Fabrizio and Atangana-Baleanu fractional derivatives

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2299-2305 ◽  
Author(s):  
Ilknur Koca ◽  
Abdon Atangana
Keyword(s):  
Diffusion Equation ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Heat Diffusion ◽  
Relaxation Kernel ◽  
Extended Version ◽  
Heat Diffusion Equation ◽  
The Laplace Transform ◽  
Non Local

Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.

scholarly journals Analysis of rubella disease model with non-local and non-singular fractional derivatives

2017 ◽  
Vol 8 (1) ◽  
pp. 17-25 ◽  
Author(s):  
Ilknur Koca
Keyword(s):  
Exact Solution ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Disease Model ◽  
Time Derivative ◽  
Banach Fixed Point Theorem ◽  
Fractional Differentiation ◽  
Non Local ◽  
Time Fractional Derivative

In this paper we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this we extend the model describing the Rubella spread by replacing the time derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.

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