Existence and Stability Results on Hadamard Type Fractional Time-Delay Semilinear Differential Equations
Nazım I. Mahmudov, Areen Al-Khateeb
Abstract
A delayed perturbation of the Mittag-Leffler type matrix function with logarithm is proposed. This combines the classic Mittag–Leffler type matrix function with a logarithm and delayed Mittag–Leffler type matrix function. With the help of this introduced delayed perturbation of the Mittag–Leffler type matrix function with a logarithm, we provide an explicit form for solutions to non-homogeneous Hadamard-type fractional time-delay linear differential equations. We also examine the existence, uniqueness, and Ulam–Hyers stability of Hadamard-type fractional time-delay nonlinear equations.
Topics & Concepts
MathematicsHadamard transformLogarithmUniquenessMittag-Leffler functionApplied mathematicsMatrix functionMathematical analysisMatrix (chemical analysis)Type (biology)Nonlinear systemFractional calculusPure mathematicsSymmetric matrixEigenvalues and eigenvectorsPhysicsComposite materialQuantum mechanicsBiologyMaterials scienceEcologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsNumerical methods for differential equations