Solving inverse non-linear fractional differential equations by generalized Chelyshkov wavelets

Erman, Sertaç; Demir, Ali; Ozbilge, Ebru

doi:10.1016/j.aej.2022.10.063

Cited by 4 publications

(2 citation statements)

References 37 publications

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“…Numerical methods for solving inverse problems for fractional-order ODEs are proposed in [14,39,40]. The shooting method is employed in [14] for numerically solving terminal value problems for Caputo fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…The shooting method is employed in [14] for numerically solving terminal value problems for Caputo fractional differential equations. In [39], the authors develop a numerical method for recovering a right-hand side function of a nonlinear fractional-order ODE, using Chelyshkov wavelets. Numerical discretizations of inverse problems for Caputo fractional ODEs under interval uncertainty are constructed in [40].…”

Section: Introductionmentioning

confidence: 99%

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A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems

Koleva,

Vulkov

2024

Fractal Fract

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This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a quadratic functional, to compute the values of the unknown parameter vector. Numerical algorithm combining the method with appropriate fractional derivative approximation on graded mesh is applied to SIS and SEIR problems to illustrate the efficiency and accuracy. Tikhonov regularization is implemented to improve the convergence. Results from computations, both with noisy-free and noisy data, are provided and discussed. Simulations with real data are also performed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems

Koleva,

Vulkov

2024

Fractal Fract

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Numerical solution of fractional PDEs through wavelet approach

Yan,

Kumbinarasaiah,

Manohara

et al. 2024

Z. Angew. Math. Phys.

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To solve fractional partial differential equations (FPDEs) under various physical conditions, this study developed a novel method known as the Hermite wavelet method employing the functional integration matrix. The method that has been suggested is based on the Hermite wavelet collocation process. To determine the solution of the fractional differential equations, the Caputo fractional derivative operator of order $$\alpha \in (0,1]$$ α ∈ ( 0 , 1 ] is used. With the use of appropriate grid points, this method converts FPDEs into a system of nonlinear algebraic equations. We achieve a solution by solving these nonlinear algebraic equations by the Newton–Raphson method. Tables and graphs show that the suggested method produces superior results. We provide various illustrative examples to establish the effectiveness of the suggested concept, and the outcomes support the applicability of the suggested strategy. Obtained results are numerically expressed in terms of absolute errors. Finally, convergence analyses are discussed as some theorem with proof.

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Numerical solution of some stiff systems arising in chemistry via Taylor wavelet collocation method

Manohara,

Kumbinarasaiah

2023

J Math Chem

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Solving inverse non-linear fractional differential equations by generalized Chelyshkov wavelets

Cited by 4 publications

References 37 publications

A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems

A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems

Numerical solution of fractional PDEs through wavelet approach

Numerical solution of some stiff systems arising in chemistry via Taylor wavelet collocation method

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