A modified Laplace transform for certain generalized fractional operators

Yıl 2018, Cilt: 1 Sayı: 2, 88 - 98, 31.08.2018

Fahd Jarad Thabet Abdeljawad

Öz

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.

Anahtar Kelimeler

Generalized fractional derivatives, Generalized Caputo, convolution theorem

Kaynakça

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