On a nonlinear Volterra integrodifferential equation involving fractional derivative with Mittag-Leffler kernel
Tomás Caraballo, Tran Bao Ngoc, Nguyen Huy Tuan, Renhai Wang
Abstract
In this paper, we study a nonlinear time-fractional Volterra equation with nonsingular Mittag-Leffler kernel in Hilbert spaces. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we give a mild solution of our problem. Our main tool here is using some Sobolev embeddings.
Topics & Concepts
Invertible matrixMathematicsMittag-Leffler functionFractional calculusKernel (algebra)Sobolev spaceNonlinear systemVolterra integral equationEigenvalues and eigenvectorsApplied mathematicsVolterra equationsMathematical analysisLaplace transformPure mathematicsIntegral equationPhysicsQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods in engineering