2017/05/11 by Li Ma, Changpin Li · 1 citation
Mathematics · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Differential Equations and Boundary Problems #Hadamard transform #Mathematics #Fractional calculus #Hadamard three-lines theorem #Singularity #Semigroup #Pure mathematics #Applied mathematics #Mathematical analysis #Calculus (dental) #Hadamard matrix
paper · doi:10.1142/s0218348x17500335
openalex publication_date 2017/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
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.