A modified Laplace transform for certain generalized fractional operators

Authors : Fahd JARAD, Thabet ABDELJAWAD

Pages : 88-98

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Publication Date : 2018-08-31

Article Type : Research Paper

Abstract :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 \rho-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.
Keywords : Generalized fractional derivatives, Generalized Caputo, convolution theorem