Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 64, pp. 1-19.

Title: Existence and uniqueness of  the solution to initial and inverse problems for 
integro-differential heat equations with fractional load

Authors: Ravi P. Agarwal (Florida Institute of Tech., Melbourne, FL, USA)
         Umida Baltaeva (Urgench State Univ., Uzbekistan)
         Florence Hubert (Aix-Marseille Univ., Marseille, France)
         Boburjon Khasanov (Khorezm Mamun Academy, Khorezm, Uzbekistan)

Abstract: 
This work is devoted to the unique solvability of the direct and 
inverse problems for a multidimensional heat equation with a 
fractional load in Holder spaces. 
In the problem under consideration, the loaded term is in
the form of a fractional integral operator for the time variable.
We  prove the existence and uniqueness of the solution to these
problems by the contraction mapping theorem and the theory of
integral equations.


Submitted August 15, 2024. Published October 23, 2024.
Math Subject Classifications: 35K15, 35R30.
Key Words: Heat equation; Cauchy problem; inverse problem; loaded equation; fractional operator.