期刊
出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X17500335
关键词
Hadamard-Type Fractional Operators; Semigroup; Well-Posedness; Banach Contraction Mapping Principle; Perturbation
资金
- National Natural Science Foundation of China [11372170, 11632008]
This paper is devoted to the investigation of the Hadamard fractional calculus in three aspects. First, we study the semigroup and reciprocal properties of the Hadamard-type fractional operators. Then, the definite conditions of certain class of Hadamard-type fractional differential equations (HTFDEs) are proposed through the Banach contraction mapping principle. Finally, we prove a novel Gronwall inequality with weak singularity and analyze the dependence of solutions of HTFDEs on the derivative order and the perturbation terms along with the proposed initial value conditions. The illustrative examples are presented as well.
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