Abstract The Mittag–Leffler function is universally acclaimed as the Queen function of
fractional calculus. The aim of this work is to survey the key results and applications …

The problem of the existence and uniqueness of solutions of boundary value problems
(BVPs) for a nonlinear fractional differential equation of order 2< α≤ 3 is studied. The BVP is …

Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …

Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained
treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation …

We discuss existence, uniqueness, and structural stability of solutions of nonlinear
differential equations of fractional order. The differential operators are taken in the Riemann …

In this paper, we find the solution of the time-fractional Newell-Whitehead-Segel equation
with the help of two different methods. The newell-Whitehead-Segel equation plays an …

By the beginning of November 2008, the International Workshops on New Trends in Science
and Technology (NTST 08) and Fractional Differentiation and its Applications (FDA08) were …

2.1 Integral transforms.......................... 5 2.1. 1 Laplace transform...................... 5 2.1. 2
Exponential Fourier transform............... 8 2.1. 3 Sin-Fourier transform.................... 10 2.1. 4 …

In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear
fractional differential equation boundary value problem: where 1< α⩽ 2 is a real number …