The present paper aims at the study and derivation of Saigo generalized fractional integral operator involving product of Hfunction of one variable and general class of polynomials. On account of the most general nature of the operator, H-function and general class of polynomials occurring in the main result, a large number of known and new results involving Rieman-Liouville, ErdélyiKober Fract...

*Correspondence: [email protected] 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK Full list of author information is available at the end of the article Abstract We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fract...

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...

It has been shown that anomalous relaxation in dielectrics can be described in terms of equations with fractional derivatives. The solutions of the resulting equation with fractional derivatives are expressed by the Mittag –Leffler function and the Fox function. The conditions of a change from the Debye relaxation to “slow” (anomalous) relaxation with a power time dependence have been examined ...

Symmetry is a fascinating property of numerous mathematical notions. In analysis function f:[a,b]→R symmetric about a+b2 satisfies the equation f(a+b−x)=f(x). this paper, we investigate relationship unified Mittag–Leffler with some known special functions. We have obtained integral transforms in terms Wright generalized function. also established recurrence relation along another important resu...