Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation
M. A. Sultanov, D. K. Durdiev, Askar Rahmonov
Abstract
In this work, an explicit solution of the initial-boundary value problem for a multidimensional time-fractional differential equation is constructed. The possibility of obtaining this equation from an integro-differential wave equation with a Mittag–Leffler–type memory kernel is shown. An explicit solution to the problem under consideration is obtained using the Laplace and Fourier transforms, the properties of the Fox H-functions and the convolution theorem.
Topics & Concepts
MathematicsLaplace transformMathematical analysisDifferential equationBoundary value problemKernel (algebra)Convolution (computer science)Partial differential equationIntegro-differential equationLaplace's equationGreen's function for the three-variable Laplace equationInitial value problemFractional calculusFirst-order partial differential equationHomogeneous differential equationUniversal differential equationConvolution theoremFourier transformApplied mathematicsExact differential equationFourier analysisOrdinary differential equationPure mathematicsFractional Fourier transformComputer scienceArtificial neural networkDifferential algebraic equationMachine learningFractional Differential Equations SolutionsDifferential Equations and Boundary ProblemsDifferential Equations and Numerical Methods