GENERALIZED LAPLACE TRANSFORM AND TEMPERED Ψ-CAPUTO FRACTIONAL DERIVATIVE
Milan Medveď, Michal Pospíšil
Abstract
In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived. The results are applied to find a solution to an initial value problem for a nonhomogeneous linear fractional differential equation with the tempered Ψ-Caputo fractional derivative of an order α for n− 1 <α<n N. An illustrative example is given for 0 <α<1 comparing solutions to the same initial value problem but with different tempering and Ψ.
Topics & Concepts
Laplace transformFractional calculusMathematicsDerivative (finance)Applied mathematicsMathematical analysisInitial value problemOrder (exchange)Value (mathematics)StatisticsFinanceEconomicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisIterative Methods for Nonlinear Equations