Approximate controllability for systems of fractional nonlinear differential equations involving Riemann-Liouville derivatives

In this research, the Magnetohydrodynamic flow model within a porous vessel containing blood was examined. What makes this study intriguing is the inclusion of a fractional-order derivative term in the Magnetohydrodynamic flow system equations. Fractional derivatives were chosen for their ability to encompass both integer and fractional-order derivatives, leading to more realistic modeling results. The numerical solution for the partial differential equation system was obtained using the finite differences method. Solutions were derived using both central difference and backward difference approaches to enhance the reliability of the results. The Grünwald-Letnikov derivative approach was employed for the fractional derivative term, while the Crank-Nicolson method was applied for other terms. Solutions were obtained for velocity, temperature, and concentration profiles. Subsequently, a thorough analysis was conducted to investigate variations in these solutions for changing values of significant flow parameters such as Hartmann number, Grashof number, solute Grashof number, a small positive constant, radiation parameter, Prandtl number, and Schmidt number. Additionally, the study analyzed changes in the fractional derivative order. Finally, the impact of flow parameters on flow in a non-porous medium was investigated, and the results were presented graphically. The study highlighted the significant effects of various parameters on blood flow.

Section: Introductionmentioning

confidence: 99%

Fractional model for blood flow under MHD influence in porous and non-porous media

Ayaz,

Heredağ

2024

“…Recently, FC started to penetrate the domain of control theory [10,13,14]; in particular, it is used to investigate the notion of regional observability; see [15][16][17][18] for linear fractional systems and [19,20] for semilinear ones. In this paper, we investigate the notion of regional boundary observability, which is basically regional observability where the desired subregion is a part of the boundary of the evolution domain [21,22].…”

Section: Introductionmentioning

confidence: 99%

On the regional boundary observability of semilinear time-fractional systems with Caputo derivative

Zguaid

Alaoui

2023

This paper considers the regional boundary observability problem for semilinear time-fractional systems. The main objective is to reconstruct the initial state on a subregion of the boundary of the evolution domain of the considered fractional system using the output equation. We proceed by providing a link between the regional boundary observability of the considered semilinear system on the desired boundary subregion, and the regional observability of its linear part, in a well chosen subregion of the evolution domain. By adding some assumptions on the nonlinear term appearing in the considered system, we give the main theorem that allows us to reconstruct the initial state in the well-chosen subregion using the Hilbert uniqueness method (HUM). From it, we recover the initial state on the boundary subregion. Finally, we provide a numerical example that backs up the theoretical results presented in this paper with a satisfying reconstruction error.

Controllability of nonlinear fractional integrodifferential systems involving multiple delays in control

Haq,

Sukavanam

2024

Self Cite

This work studies the existence of solutions and approximate controllability of fractional integrodifferential systems with Riemann-Liouville derivatives and with multiple delays in control. We establish suitable assumptions to prove the existence of solutions. Controllability of the system is shown by assuming a range condition on control operators and Lipschitz condition on non-linear functions. We use the concepts of strongly continuous semigroup rather than resolvent operators. Finally, an example is give to illustrate the theory.