We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving six parameters truncated Mittag–Leffler function Gamma function. In view of these, we obtain some integral inequalities Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, Grüss type to calculus.

Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward ...

1050 NOTICES OF THE AMS VOLUME 46, NUMBER 9 T his year marks the thirtieth anniversary of the realization of the dream of one Swedish mathematician. In 1916, on his seventieth birthday, Gösta Mittag-Leffler promised his and his wife’s considerable fortune to the goal of founding a mathematics institute. More than forty years had to pass after his death before the institute was launched in earne...

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...

We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called Mittag-Leffler–Galerkin method—comprises finite Mittag-Leffler function and Galerkin method. error analysis of method was studied. As result, we two theorems by which can be bounded. In addition analysis, residual correction method, allows us estimate obtain approximate ...

Using the results of third-order differential subordination, we introduce certain families admissible functions and discuss some applications subordination for meromorphic associated with a linear operator containing generalized Mittag-Leffler function.

We propose a method for determining the solution and source term of a generalized timefractional diffusion equation. The method is based on selecting a bi-orthogonal basis of L space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag–Leffler...

We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities a...