On a nonlocal problem for a Caputo time‐fractional pseudoparabolic equation
Nguyễn Anh Tuấn, Zakia Hammouch, Erdal Karapınar, Nguyen Huy Tuan
Abstract
In this paper, we consider a class of pseudoparabolic equations with the nonlocal condition and the Caputo derivative. Two cases of problems (1–2) will be studied, which are linear case and nonlinear case. For the first case, we establish the existence, the uniqueness, and some regularity results by using some estimates technique and Sobolev embeddings. Second, the Banach fixed‐point theorem will be applied to the nonlinear case to prove the existence and the uniqueness of the mild solution.
Topics & Concepts
MathematicsUniquenessFixed-point theoremSobolev spaceNonlinear systemClass (philosophy)Banach fixed-point theoremFractional calculusMathematical analysisApplied mathematicsBanach spacePure mathematicsPhysicsComputer scienceArtificial intelligenceQuantum mechanicsFractional Differential Equations SolutionsDifferential Equations and Boundary ProblemsNonlinear Differential Equations Analysis