Checking the Regularity of the Linear Method of Summation Fourier Series

A unique solvability of the inverse initial problem for a time-degenerate fractional partial differential equation is proved. Using the method of variable separation, we obtain the Cauchy problem for the fractional differential equation involving the bi-ordinal Hilfer derivative in the time variable. The authors present the solution to this Cauchy problem in an explicit form via the Kilbas–Saigo function. Further, using the upper and lower bounds of this function, the authors prove the uniform convergence of the infinite series corresponding to the solution of the formulated inverse initial problem. Keywords: inverse-initial problem, degenerate PDE, bi-ordinal Hilfer operator, Kilbas–Saigo function.

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A Necessary Condition for the Convergence of the Fourier Transform

Tovkach,

Medvid

2024

KCA

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The authors show that the Fourier transform plays an important role in many applied problems of system analysis. Its properties are analyzed, which directly affect the efficiency of using the optimal decision theory in the problems. The necessary condition for the convergence of the Fourier transform is established, which provides a powerful tool for its use in the implementation of practical problems. Keywords: Fourier transform, system analysis, theory of optimal solutions, necessary convergence conditions.

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Checking the Regularity of the Linear Method of Summation Fourier Series

Cited by 3 publications

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A Necessary Condition for the Convergence of the Fourier Transform

A Necessary Condition for the Convergence of the Fourier Transform

Inverse-Initial Problem for Time-Degenerate Pde Involving the Bi-Ordinal Hilfer Derivative

A Necessary Condition for the Convergence of the Fourier Transform

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