Browsing by Author "Thabet, Abdeljawad"

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A modified Laplace transform for certain generalized fractional operators
(2018) Jarad, Fahd; Thabet, Abdeljawad
It is known that Laplace transform converges for functions of exponential order. In order to extend the possibility of working in a large class of functions, we present a modified Laplace transform that we call ρ-Laplace transform, study its properties and prove its own convolution theorem. Then, we apply it to solve some ordinary differential equations in the frame of a certain type generalized fractional derivatives. This modified transform acts as a powerful tool in handling the kernels of these generalized fractional operators