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Well-Posedness of General Time-Fractional Diffusion Equations Involving Atangana-Baleanu Derivative |
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PP: 107-117 |
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doi:10.18576/pfda/090108
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Author(s) |
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Soraya Abdelaziz,
Nabil Shawagfeh,
Mohammed Al-Refai,
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Abstract |
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| In this paper, we study a general time-fractional diffusion equation involving the Atangana-Baleanu derivative of Caputo sense. First, we derive weak maximum-minimum principles to the associated fractional differential operators of the parabolic type, then we apply these principles to establish uniqueness and stability results to initial-boundary value problem and to obtain a norm estimate of the solution. For the existence of solution to the problem, we apply the eigenfunction expansion method to construct a formal solution, which under certain conditions proved to be a weak solution.
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