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## A modifi ed Laplace transform for certain generalized fractional operators

#### Fahd JARAD [1] , Thabet ABDELJAWAD [2]

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 modied Laplace

transform that we call \rho-Laplace transform, study its properties and prove its own convolution the-

orem. Then, we apply it to solve some ordinary differential equations in the frame of a certain type

generalized fractional derivatives. This modied transform acts as a powerful tool in handling the

kernels of these generalized fractional operators.

Generalized fractional derivatives, Generalized Caputo
 Bibtex @research article { rna452424, journal = {Results in Nonlinear Analysis}, issn = {}, eissn = {2636-7556}, address = {}, publisher = {Erdal KARAPINAR}, year = {2018}, volume = {1}, pages = {88 - 98}, doi = {}, title = {A modifi ed Laplace transform for certain generalized fractional operators}, key = {cite}, author = {Jarad, Fahd and Abdeljawad, Thabet} } APA Jarad, F , Abdeljawad, T . (2018). A modifi ed Laplace transform for certain generalized fractional operators . Results in Nonlinear Analysis , 1 (2) , 88-98 . Retrieved from https://dergipark.org.tr/en/pub/rna/issue/37067/452424 MLA Jarad, F , Abdeljawad, T . "A modifi ed Laplace transform for certain generalized fractional operators" . Results in Nonlinear Analysis 1 (2018 ): 88-98 Chicago Jarad, F , Abdeljawad, T . "A modifi ed Laplace transform for certain generalized fractional operators". Results in Nonlinear Analysis 1 (2018 ): 88-98 RIS TY - JOUR T1 - A modifi ed Laplace transform for certain generalized fractional operators AU - Fahd Jarad , Thabet Abdeljawad Y1 - 2018 PY - 2018 N1 - DO - T2 - Results in Nonlinear Analysis JF - Journal JO - JOR SP - 88 EP - 98 VL - 1 IS - 2 SN - -2636-7556 M3 - UR - Y2 - 2018 ER - EndNote %0 Results in Nonlinear Analysis A modifi ed Laplace transform for certain generalized fractional operators %A Fahd Jarad , Thabet Abdeljawad %T A modifi ed Laplace transform for certain generalized fractional operators %D 2018 %J Results in Nonlinear Analysis %P -2636-7556 %V 1 %N 2 %R %U ISNAD Jarad, Fahd , Abdeljawad, Thabet . "A modifi ed Laplace transform for certain generalized fractional operators". Results in Nonlinear Analysis 1 / 2 (August 2018): 88-98 . AMA Jarad F , Abdeljawad T . A modifi ed Laplace transform for certain generalized fractional operators. RNA. 2018; 1(2): 88-98. Vancouver Jarad F , Abdeljawad T . A modifi ed Laplace transform for certain generalized fractional operators. Results in Nonlinear Analysis. 2018; 1(2): 88-98.