The linear operator c + (??)?/2, where > 0 and (??)?/2 is the fractional Laplacian on periodic domain, arises in existence of travelling waves Korteweg-de Vries equation. We establish a relation Green function this with Mittag-Leffler function, which was previously used context Riemann-Liouville Caputo derivatives. By using relation, we prove that strictly positive single-lobe (monotonically de...

Abstract. This paper deals with the solution of unified fractional reactiondiffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. On account of the most general character of the derived results, numerous results on fractional reaction, fractional diffusi...

Abstract In a recent paper, Saxena et al.[1] developed the solutions of three generalized fractional kinetic equations in terms of the Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized fractional kinetic equations. The results are obtained in a compact form in terms of generalized Mittag-Leffler functions. Their relation to fundam...

A non-Arrhenius model based on the Mittag-Leffler function has been conceived as a basic concept. This approach allows modelling both sub-Arrhenius and super-Arrhenius behaviours giving rise to modified temperature integrals.

In this paper, we study the asymptotic stability of three fractional scalar systems by using the method of universal adaptive stabilization: (I) Fractional dynamics with integer-order control strategy, (II) Fractional dynamics with fractional control strategy, and (III) Application of fractional viscoelastic and electromagnetic theories in universal adaptive stabilization. It is shown that the ...

We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize...

This paper deals with a new mathematical model of the hamstring muscle group. The proposed viscoelastic model includes fractional derivatives of stretching force and elongation as well as restrictions on the coefficients that follow from the second law of thermodynamics. On the basis of experimental data four coefficients of the model have been calculated by numerical procedure. Obtained result...

We consider a partial differential equation associated with a mathematical model describing the concentration of nutrients in blood which interferes directly on the erythrocyte sedimentation rate in the case of an average fluid velocity equal to zero. Introducing the fractional derivative in the Caputo sense, we propose a time-fractional mathematical model which contains, as a particular case, ...

Introduction/purpose: Certain integrals involving the generalized Mittag-Leffler function with different types of polynomials are established. Methods: The properties used in conjunction kinds such as Jacobi, Legendre, and Hermite order to evaluate their integrals. Results: Some integral formulae Legendre function, Bessel Maitland hypergeometric functions derived. Conclusions: results obtained ...

In this paper, we consider the Le Roy-type Mittag-Leffler function. Our main focus is to establish some sufficient conditions so that normalized Le-Roy type function posses geometric properties such as starlikeness, convexity, close-to-convexity (univalency) and uniformly convexity inside unit disk. Using these results, of are derived application. Results obtained in paper new. Interesting cons...