A theoretical framework for analyzing stochastic data from single-particle tracking in viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation, we found analytical expressions for the two-time dynamics of a particle subjected to a harmonic potential. The mean-square displacement and the velocity autocorrelation function ...

This paper deals with the study of linear systems of fractional differential equations such as the following system: 0096-3 doi:10 * Co E-m Y ða 1⁄4 AðxÞY þ BðxÞ; ð1Þ where Y ða is the Riemann–Liouville or the Caputo fractional derivative of order a (0 < a 5 1), and AðxÞ 1⁄4 a11ðxÞ a1nðxÞ . . . . . . . . . an1ðxÞ annðxÞ 0BBBBBB@ 1CCCCCCA; BðxÞ 1⁄4 b1ðxÞ . . . . . . . . . bnðxÞ 0BBBBBB@ 1CCCCCCA...

The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Hückel linearization, the analytical solutions ...

*Correspondence: [email protected] 2College of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China 3Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, 710049, China Full list of author information is available at the end of the article Abstract This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg ...

We investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuousstate branching theory. In particular, this equation governs the evolution of the Lévy measure of a critical continuous-state branching process which becomes extinct (i.e., is absorbed at zero) alm...

By observing that the fractional Caputo derivative of order α ∈ (0, 1) can be expressed in terms a multiplicative convolution operator, we introduce and study class such operators which also have same self-similarity property as derivative. We proceed by identifying subclass is bijection with set Bernstein functions provide several representations their eigenfunctions, corresponding function, g...

Abstract. In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t),...

This paper studies a prototype of inverse obstacle scattering problems whose governing equation is the Helmholtz equation in two dimensions. An explicit method to extract information about the location and shape of unknown obstacles from the far field operator with a fixed wave number is given. The method is based on: an explicit construction of a modification of Mittag-Leffler’s function via t...

This research aims to present a linear operator Lp,q?,?,?f utilizing the q-Mittag–Leffler function. Then, we introduce subclass of harmonic (p,q)-convex functions HTp,q(?,W,V) related Janowski For p-valent f class, investigate geometric properties, such as coefficient estimates, convex combination, extreme points, and Hadamard product. Finally, closure property is derived using under q-Bernardi...