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Remarks on the Systems of Semilinear Fractional Rayleigh‐Stokes Equation

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  • Le Dinh Long

Abstract

In this paper, we study the Cauchy problem for a system of Rayleigh‐Stokes equations. In this system of equations, we use derivatives in the classical Riemann‐Liouville sense. This system has many applications in some non‐Newtonian fluids. We obtained results for the existence, uniqueness, and frequency of the solution. We discuss the stability of the solutions and find the solution spaces. Our main technique is to use the Banach mapping theorem combined with some techniques in Fourier analysis.

Suggested Citation

  • Le Dinh Long, 2021. "Remarks on the Systems of Semilinear Fractional Rayleigh‐Stokes Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6880435
    DOI: 10.1155/2021/6880435
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    1. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Acay, Bahar & Inc, Mustafa, 2021. "Fractional modeling of temperature dynamics of a building with singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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