Abstract In this paper, we present the monotonicity analysis for nabla fractional differences with discrete generalized Mittag-Leffler kernels $( {}^{ABR}_{a-1}{\nabla }^{\delta ,\gamma }y )(\eta )$ (a−1A</mm...

In the current paper, we consider multi-derivative nonlinear fractional differential equations involving Atangana-Baleanu derivative. We investigate fundamental results about existence, uniqueness, boundedness and dependence of solution on various data. The analysis is based a integral operator due to T. R. Prabhakar generalized Mittag-Leffler function, Krasnoselskii’s fixed point theorem Gronw...

In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to generalized regularized long wave equations a new fractional operator obtain approximate solutions. We classical differential form by using Atangana-Baleanu derivative which defined Mittag-Leffler function. To show efficiency of proposed method, numerical example given for different v...

After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each oth...