New Generalized Results for Modified Atangana-Baleanu Fractional Derivatives and Integral Operators

In this current study, first we establish the modified power Atangana-Baleanu fractional derivative operators (MPC) in both the Caputo and Riemann-Liouville (MPRL) senses. Using the convolution approach and Laplace transformation, the so-called modified power fractional Caputo and R-L derivative operators with non-singular kernels are introduced. We establish the boundedness of the modified Caputo fractional derivative operator in this study. The fractional differential equations are solved with the generalised Laplace transform (GLT). In addition, the corresponding form of the fractional integral operator is defined. Also, we prove the boundedness and Laplace transform of the fractional integral operator. The composition of power fractional derivative and integral operators is given in the study. Additionally, several examples related to our findings along with their graphical representation are presented.