On an initial value problem for time fractional pseudo‐parabolic equation with Caputo derivative
Nguyen Hoang Luc, Hossein Jafari, Poom Kumam, Nguyen Huy Tuan
Abstract
In this paper, we consider a pseudo‐parabolic equation with the Caputo fractional derivative. We study the existence and uniqueness of a class of mild solutions of these equations. For a nonlinear problem, we first investigate the global solution under the initial data u 0 ∈ L 2 . In the case of initial data u 0 ∈ L q , q ≠ 2, we obtain the local existence result. Our main tool here is using fundamental tools, namely, Banach fixed point theorem and Sobolev embeddings. In addition, we give an example to illustrate the effectiveness of the method has been proposed.
Topics & Concepts
MathematicsUniquenessInitial value problemFixed-point theoremFractional calculusSobolev spaceBanach fixed-point theoremNonlinear systemMathematical analysisParabolic partial differential equationDerivative (finance)Class (philosophy)Banach spaceApplied mathematicsPartial differential equationComputer scienceArtificial intelligencePhysicsEconomicsFinancial economicsQuantum mechanicsFractional Differential Equations SolutionsNumerical methods in engineeringDifferential Equations and Boundary Problems