New aspects of time fractional optimal control problems within operators with nonsingular kernel

Yıldız, Tuğba Akman; Jajarmi, Amin; Yıldız, Burak; Băleanu, Dumitru

doi:10.3934/dcdss.2020023

Cited by 50 publications

(7 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where x n (t) = ∑ n j=1 Ψ n (t) and y n (t) = ∑ n j=1 Φ n (t). By taking the norm of both sides of Equation ( 24), we have (25) Since the kernels satisfy the Lipschitz condition (see Theorem 2), we get…”

Section: Qualitative Properties Of the P-pmmentioning

confidence: 99%

“…Because of effective properties, fractional order calculus has found wide applications to model dynamics processes in many well-known fields, such as biology [6][7][8][9][10][11], physics [12][13][14][15][16], finance and economics [17,18], science and engineering [19,20], mechanics and mathematical modeling [21,22]. We enumerate numerous fractional operators in the literature [23][24][25][26][27]. Moreover, some numerical and approximate solution methods and their illustrative applications have been stated in .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate

2020

View full text Add to dashboard Cite

In this work, a fractional predator-prey model with the harvesting rate is considered. Besides the existence and uniqueness of the solution to the model, local stability and global stability are experienced. A novel discretization depending on the numerical discretization of the Riemann–Liouville integral was introduced and the corresponding numerical discretization of the predator–prey fractional model was obtained. The net reproduction number R 0 was obtained for the prediction and persistence of the disease. The dynamical behavior of the equilibria was examined by using the stability criteria. Furthermore, numerical simulations of the model were performed and their graphical representations are shown to support the numerical discretizations, to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary order derivative. In our investigations, the fractional operator is understood in the Caputo sense.

show abstract

Section: Qualitative Properties Of the P-pmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate

2020

View full text Add to dashboard Cite

show abstract

“…The variational approach has been applied to obtain the necessary optimality and transversality conditions for solving the FOCPs by Chiranjeevi T, et al 11 . Caputo-Fabrizio FD was used in a formulation of time FOCPs and deriving the optimality system in terms of Volterra integrals by Yildiz, T A, et al 12 and for more about studying the FOCPs (see 13,14 ). Also, it is possible to see articles that provide a study of solving fractional order Volterra-Fredholm integral equations 15,16 .…”

Section: Introductionmentioning

confidence: 99%

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

Holel

Hasan²

2023

Baghdad Sci.J

View full text Add to dashboard Cite

The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

show abstract

“…They derive necessary optimality conditions and propose an efficient method for solving, numerically, these problems. Yıldız et al [64] formulate new time FOCPs governed by Caputo-Fabrizio FD. To solve these problems, they firstly convert them into Volterra-type systems and then apply a new numerical scheme based on the approximation of Volterra integrals.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov functions for fractional-order systems in biology: Methods and applications

Boukhouima

Hattaf

Lotfi

et al. 2020

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

We prove new estimates of the Caputo derivative of order α ∈ (0, 1] for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.

show abstract

New aspects of time fractional optimal control problems within operators with nonsingular kernel

Cited by 50 publications

References 54 publications

Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate

Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

Lyapunov functions for fractional-order systems in biology: Methods and applications

Contact Info

Product

Resources

About