Inverse Problem of Determining the Source of the Heat Equation with Fractional Time Derivatives
DOI:
https://doi.org/10.58649/cs160p94Keywords:
Fractional time equation, Fractional derivative, Fourier method, Mittag-Leffler function, Bessel inequality, Inverse problem, Integral equation, VolterraAbstract
In this paper, we study a linear inverse problem for a heat conductivity equation with fractional time derivatives with overdetermination conditions at an interior point. First, we study the direct problem. Using the Fourier method, this direct problem is reduced to an equivalent integral equation. Then, using estimates of the Mittag-Leffler function and some of its properties, the inverse problem is reduced to an equivalent a linear system of integral equations. To solve this system, the Volterra integral equation method is used. Global theorems of existence and uniqueness of the solution of the inverse problem under consideration are proved.
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