Properties of a Partial Fredholm Integro-differential Equations with Nonlocal Condition and Algorithms
Dzhumabaev D.S. Dzhumabaev A.D. Assanova A.T.
September 2024Birkhauser
Mediterranean Journal of Mathematics
2024#21Issue 6
The paper is concerned with a nonlocal problem for a partial Fredholm integro-differential equation (IDE) of hyperbolic type is investigated. This problem is reduced to a problem containing a family of boundary value problems for the ordinary Fredholm IDEs and some integral relationships. A novel concept of general solution to a family of the ordinary Fredholm IDEs is introduced, and its properties are discussed. A necessary and sufficient condition for the well-posedness of the nonlocal problem for the partial Fredholm integro-differential equation (IDE) of hyperbolic type is obtained, and an algorithm for finding its solution is offered.
34K10 , 35L53 , 35R09 , 45J05 , 45K05 , algorithm , nonlocal problem , Partial Fredholm integro-differential equation of hyperbolic type , well-posedness criterion , ΔN(ω) general solution
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