Parsimonious Continuous Time Random Walk Models and Kurtosis for Diffusion in Magnetic Resonance of Biological Tissue [PDF]
Frontiers in Physics, 2015 In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue.
Carson eIngo +5 more
doaj +3 more sources
Integral representations of Mittag-Leffler function on the positive real axis
Trends in Computational and Applied Mathematics, 2019 The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N.
Eliana Contharteze Grigoletto +2 more
doaj +1 more source
Fractional operators with generalized Mittag-Leffler k-function
Advances in Difference Equations, 2019 In this paper, our main aim is to deal with two integral transforms involving the Gauss hypergeometric functions as their kernels. We prove some composition formulas for such generalized fractional integrals with Mittag-Leffler k-function.
Shahid Mubeen, Rana Safdar Ali
doaj +1 more source
Certain Properties Associated with Generalized $M$-Series using Hadamard Product [PDF]
Sahand Communications in Mathematical AnalysisThe generalized $M$-series is a hybrid function of generalized Mittag-Leffler function and generalized hypergeometric function. The principal aim of this paper is to investigate certain properties resembling those of the Mittag-Leffler and ...
Dheerandra Sachan +2 more
doaj +1 more source
Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function. [PDF]
Adv Differ Equ, 2021 Khan A +5 more
europepmc +1 more source
Generalized Langevin Equation and the Prabhakar Derivative
Mathematics, 2017 We consider a generalized Langevin equation with regularized Prabhakar derivative operator. We analyze the mean square displacement, time-dependent diffusion coefficient and velocity autocorrelation function.
Trifce Sandev
doaj +1 more source
Fractional Integral Inequalities of Gruss Type via Generalized Mittag-Leffler Function
International Journal of Analysis and Applications, 2019 We use generalized fractional integral operator containing the generalized Mittag-Leffler function to establish some new integral inequalities of Gr¨uss type. A cluster of fractional integral inequalities have been identified by setting particular values
G. Farid +3 more
doaj +2 more sources
A Generalized q-Mittag-Leffler Function by q-Captuo Fractional Linear Equations
Abstract and Applied Analysis, 2012 Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions.
Thabet Abdeljawad +2 more
doaj +1 more source
A study of generalized Mittag-Leffler-type function of arbitrary order
Demonstratio MathematicaWe present a novel generalized Mittag-Leffler-type function of arbitrary order in this study. We look into its fundamental characteristics, such as differential formulas, recurrence relations, integral representations, the Euler, Laplace, Mellin ...
Bin-Saad Maged, Younis Jihad
doaj +1 more source
Turán type inequalities for generalized Mittag-Leffler function. [PDF]
J Inequal Appl, 2017 Dou XK, Yin L.
europepmc +1 more source