Solvability of Mixed Problems for a Fourth-Order Equation with Involution and Fractional Derivative
Mokhtar Kirane, Abdissalam Sarsenbi
Abstract
In the present work, two-dimensional mixed problems with the Caputo fractional order differential operator are studied using the Fourier method of separation of variables. The equation contains a linear transformation of involution in the second derivative. The considered problem generalizes some previous problems formulated for some fourth-order parabolic-type equations. The basic properties of the eigenfunctions of the corresponding spectral problems, when they are defined as the products of two systems of eigenfunctions, are studied. The existence and uniqueness of the solution to the formulated problem is proved.
Topics & Concepts
MathematicsUniquenessEigenfunctionInvolution (esoterism)Mathematical analysisDifferential operatorFractional calculusSeparation of variablesPartial differential equationLinear mapApplied mathematicsPure mathematicsEigenvalues and eigenvectorsPhysicsLawPolitical scienceQuantum mechanicsPoliticsDifferential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsFractional Differential Equations Solutions