Results 41 to 50 of about 9,574,302 (235)

Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials

Applied Sciences, 2020
In the present paper, we numerically simulate fractional-order model of the Bloch equation by using the Jacobi polynomials. It arises in chemistry, physics and nuclear magnetic resonance (NMR).
Harendra Singh, H. Srivastava
semanticscholar   +1 more source

Fractional-Order Orthogonal Jacobi Function-Based Operational Approach for Multi-Term Diffusion-Wave Equations of Fractional Order

Fractal and Fractional
Solving fractional differential equations using spectral collocation methods based on classical orthogonal polynomials often leads to a reduced convergence rate due to the limited regularity of the solutions.
Amal Alshabanat, Mohamed A. Saker, Hanaa Moussa, Samer S. Ezz-Eldien   +3 more
doaj   +1 more source

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Applied Mathematical Modelling, 2020
The dynamic analysis of viscoelastic pipes conveying fluid is investigated by the variable fractional order model in this article. The nonlinear variable fractional order integral-differential equation is established by introducing the model into the ...
Yuanhui Wang, Yi-Ming Chen
semanticscholar   +1 more source

Fractional order differentiation by integration with Jacobi polynomials [PDF]

, 2012
International audienceThe differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess. This paper generalizes this method from the integer order to the fractional order for estimating the fractional ...
Laleg-Kirati, Taous-Meriem, Gibaru, Olivier, Perruquetti, Wilfrid, Liu, Da-Yan   +3 more
core   +3 more sources

Appell Type Changhee Polynomials Operational Matrix of Fractional Derivatives and its Applications

Eurasian Journal of Science and Engineering, 2022
In this paper, a fractional order differential equation (FDEs), will be solved numerically through a new approximative technique based on Appell type Changhee polynomials.
Abdulnasir Isah
doaj   +1 more source

Vieta–Lucas polynomials for solving a fractional-order mathematical physics model

, 2020
In this article, a fractional-order mathematical physics model, advection–dispersion equation (FADE), will be solved numerically through a new approximative technique. Shifted Vieta–Lucas orthogonal polynomials will be considered as the main base for the
Praveen Agarwal, A. A. El-Sayed
semanticscholar   +1 more source

Analysis of discrete time schemes for milling forces control under fractional order holds [PDF]

, 2013
In this paper, discrete time model reference control schemes for practical milling using different discretization of the continuous-time plant are presented. First, a basic controller scheme is addressed where a fractional order hold with pre-fixed value
De la Sen, Manuel, Longstaff, Andrew P., De la Sen Parte, Manuel, Alan Myers, Luis Rubio, Longstaff, Andrew, Rubio, Luis, Rubio Rodriguez, Luis, Manuel De la Sen, Andrew Peter Longstaff, Longstaff, Andrew Peter, Myers, Alan   +11 more
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Shifted Genocchi Polynomials Operational Matrix for Solving Fractional Order Stiff System [PDF]

, 2021
In this paper, we solve the fractional order stiff system using shifted Genocchi poly nomials operational matrix. Different than the well known Genocchi polynomials, we shift the interval from [0, 1] to [1, 2] and name it as shifted Genocchi polynomials.
Isah, Abdulnasir
core   +1 more source

A comprehensive review on fractional-order optimal control problem and its solution

Open Mathematics, 2023
This article presents a comprehensive literature survey on fractional-order optimal control problems. Fractional-order differential equation is extensively used nowadays to model real-world systems accurately, which exhibit fractal dimensions, memory ...
Abd-Elmonem Assmaa, Banerjee Ramashis, Ahmad Shabir, Jamshed Wasim, Nisar Kottakkaran Sooppy, Eid Mohamed R., Ibrahim Rabha W., El Din Sayed M.   +7 more
doaj   +1 more source

α-Sumudu Transformation Homotopy Perturbation Technique on Fractional Gas Dynamical Equation

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023
Transformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He’s
Ali Moazzam, Adnan Shokat, Emad A. Kuffi   +2 more
doaj   +1 more source