Fractional Parabolic Systems of Vector Order

Fractional Parabolic Systems of Vector Order

We consider the Cauchy problem for a system of partial differential equations of fractional order D t B U(t, x) + A (D)U(t, x) = H(t, x), where U and H are vector-valued functions and the m × m-matrix of differential operators A (D) is triangular with elliptic operators on the diagonal. The main fea...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.284 (2), p.179-195
Hauptverfasser: Ashurov, R., Sulaymonov, I.
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Cauchy problems
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial differential equations
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Sulaymonov, I.
description We consider the Cauchy problem for a system of partial differential equations of fractional order D t B U(t, x) + A (D)U(t, x) = H(t, x), where U and H are vector-valued functions and the m × m-matrix of differential operators A (D) is triangular with elliptic operators on the diagonal. The main feature of this system is that the vector order B has different components β j ∈ (0, 1] which are not necessarily rational. We find sufficient (and necessary in some cases) conditions on the initial function and right-hand side of the equation that guarantee the existence of the classical solution.
doi_str_mv 10.1007/s10958-024-07342-3
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Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial differential equations
title Fractional Parabolic Systems of Vector Order
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