Fractional abstract Cauchy problem with order $\alpha \in (1,2)$

Abstract

In this paper, we deal with a class of fractional abstract Cauchy problems of order α ∈ (1, 2) by introducing an operator Sα which is defined in terms of the Mittag-Leffler function and the curve integral. Some nice properties of the operator Sα are presented. Based on these properties, the existence and uniqueness of mild solution and classical solution to the inhomogeneous linear and semilinear fractional abstract Cauchy problems is established accordingly. The regularity of mild solution of the semilinear fractional Cauchy problem is also discussed. Contents 157 3. Properties of Operator S α (t) 159 4. Linear Problem 165 5. Nonlinear Problem 169 6. An Example 175 Acknowledgments 176 References 176

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