The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

Peng, Li; Zhou, Yong

doi:10.1007/s12346-023-00897-7

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…Differential equations with fractional derivatives play a pivotal role across a wide spectrum of fields such as the natural sciences, engineering, biological sciences, finance, and physics, capturing the interest of numerous scholars [1][2][3][4][5][6][7]. The phenomenon of time delay, a ubiquitous occurrence in the fabric of real-life scenarios, has spurred a significant body of research.…”

Section: Introductionmentioning

confidence: 99%

Existence of Mild Solutions to Delay Diffusion Equations with Hilfer Fractional Derivative

Jin,

He,

Wang

et al. 2024

Fractal Fract

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Because of the prevalent time-delay characteristics in real-world phenomena, this paper investigates the existence of mild solutions for diffusion equations with time delays and the Hilfer fractional derivative. This derivative extends the traditional Caputo and Riemann–Liouville fractional derivatives, offering broader practical applications. Initially, we constructed Banach spaces required to handle the time-delay terms. To address the challenge of the unbounded nature of the solution operator at the initial moment, we developed an equivalent continuous operator. Subsequently, within the contexts of both compact and non-compact analytic semigroups, we explored the existence and uniqueness of mild solutions, considering various growth conditions of nonlinear terms. Finally, we presented an example to illustrate our main conclusions.

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Section: Introductionmentioning

confidence: 99%

Existence of Mild Solutions to Delay Diffusion Equations with Hilfer Fractional Derivative

Jin,

He,

Wang

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

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The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

Peng,

Zhou

2023

Qual. Theory Dyn. Syst.

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Numerical treatment of the fractional Rayleigh-Stokes problem using some orthogonal combinations of Chebyshev polynomials

Abd-Elhameed,

Al-Sady,

Alqubori

et al. 2024

MATH

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<p>This work aims to provide a new Galerkin algorithm for solving the fractional Rayleigh-Stokes equation (FRSE). We select the basis functions for the Galerkin technique to be appropriate orthogonal combinations of the second kind of Chebyshev polynomials (CPs). By implementing the Galerkin approach, the FRSE, with its governing conditions, is converted into a matrix system whose entries can be obtained explicitly. This system can be obtained by expressing the derivatives of the basis functions in terms of the second-kind CPs and after computing some definite integrals based on some properties of CPs of the second kind. A thorough investigation is carried out for the convergence analysis. We demonstrate that the approach is applicable and accurate by providing some numerical examples.</p>

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The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

Cited by 3 publications

References 32 publications

Existence of Mild Solutions to Delay Diffusion Equations with Hilfer Fractional Derivative

Existence of Mild Solutions to Delay Diffusion Equations with Hilfer Fractional Derivative

The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

Numerical treatment of the fractional Rayleigh-Stokes problem using some orthogonal combinations of Chebyshev polynomials

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