TY - JOUR
AU - Gohar, Abdelrahman
AU - Younes, Mayada
AU - Doma, Salah
PY - 2024/06/22
Y2 - 2024/08/11
TI - On Gohar Fractional Calculus
JF - Journal of Fractional Calculus and Nonlinear Systems
JA - J Frac Calc & Nonlinear Sys
VL - 5
IS - 1
SE - Articles
DO - 10.48185/jfcns.v5i1.1048
UR - https://www.sabapub.com/index.php/jfcns/article/view/1048
SP - 32-51
AB - <p>Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.</p>
ER -