Generalized Laplace transform and tempered Ψ-Caputo fractional derivative
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.
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