Abstract The main aim of this paper is to investigate various types Ulam stability and Mittag-Leffler linear differential equations first order with constant coefficients using the Aboodh transform method. We also obtain Hyers–Ulam constants these some examples illustrate our results are given.

The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of sexuality. The existence of unique solution is investigated and numerical solution is provided.

The main aim of this paper is to establish two generalized integral formulas involving the extended Mittag-Leffler function based on the well known Lavoie and Trottier integral formula and the obtain results are express in term of extended Wright-type function. Also, we establish certain special cases of our main result.

Classes of coherent states are presented by replacing the labeling parameter z of Klauder-Perelomov type coherent states by confluent hypergeometric functions with specific parameters. Temporally stable coherent states for the isotonic oscillator Hamiltonian are presented and these states are identified as a particular case of the so-called Mittag-Leffler coherent states.

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems. In this paper we obtain some general integral inequalities containing generalized Mittag-Leffler function and some already known integral inequalities have been produced...

We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias is constant. When the bias depends linearly on the position, the full FPT density function is derived in terms of Hermite polynomials and generalized Mittag-...

In this paper, the solution of a class of fractional Kinetic equation involving generalized I-function has been discussed. Special cases involving the Ifunction, H-function, generalized M-series, generalized Mittag-Leffler functions are also discussed. Results obtained are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.