Existence and Uniqueness of the Solution for an Inverse Problem of a Fractional Diffusion Equation with Integral Condition
Taki-Eddine Oussaeif, Benaoua Antara, Adel Ouannas, Iqbal M. Batiha, Khaled M. Saad, Hadi Jahanshahi, Awad M. Aljuaid, Ayman A. Aly
Abstract
The solvability of the fractional partial differential equation with integral overdetermination condition for an inverse problem is investigated in this paper. We analyze the direct problem solution by using the “energy inequality” method. Using the fixed point technique, the existence and uniqueness of the solution of the inverse problem on the data are established.
Topics & Concepts
UniquenessMathematicsOverdeterminationInverse problemMathematical analysisPartial differential equationInverseDiffusionApplied mathematicsPhysicsGeometryThermodynamicsPhilosophyEpistemologyFractional Differential Equations SolutionsDifferential Equations and Boundary ProblemsNumerical methods in engineering