论文信息 - ON SOLVABILITY OF LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES∗

ON SOLVABILITY OF LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES∗

We describe a set of initial data in the abstract Cauchy problem for the linear equation with the Caputo fractional derivative and an unbounded linear closed operator A in a Banach space X Dα ∗ x(t) = Ax(t), m − 1 < α ≤ m ∈ N, dk dtk x(t)|t=0 = ξk, k = 0, . . . ,m − 1 for which the corresponding solutions can be represented by means of the MittagLeffler operator function. Some properties of the Mittag-Leffler operator function are given. Mathematics Subject Classification: primary 34G10, secondary 26A33, 45J05, 45K05

R. Gorenflo | Yuri Luchko | P. P. Zabrejko

[1] Francesco Mainardi,et al. Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics , 2012, 1201.0863.

[2] P. P. Zabrejko,et al. On the Solvability of Linear Differential Equations with Unbounded Operators in Banach Spaces , 1998 .

[3] Hari M. Srivastava,et al. The exact solution of certain differential equations of fractional order by using operational calculus , 1995 .

[4] R. Askey,et al. HANDBOOK OF INTEGRAL TRANSFORMS OF HIGHER TRANSCENDENTAL FUNCTIONS: Theory and Algorithmic Tables (Ellis Horwood Series: Mathematics and Its Applications) , 1983 .

[5] M. Caputo. Linear models of dissipation whose Q is almost frequency independent , 1966 .

[6] S. D. Eidelman,et al. Cauchy problem for evolution equations of a fractional order , 2004 .

[7] R. Gorenflo,et al. AN OPERATIONAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES , 1999 .

[8] Emilia Bazhlekova,et al. The abstract Cauchy problem for the fractional evolution equation , 1998 .