Qualitative analysis for solutions of a certain more generalized two-dimensional fractional differential system with Hadamard derivative

Analysis of nonlinear Hadamard fractional differential equations via properties of Mittag–Leffler functions

“…The continuous time random walk theory is another example of arising of fractional derivatives in description of real physical systems (see [16]). There are several existence and stability results for all kinds of Caputo and Riemann-Liouville type nonlinear FDEs with constant coefficients (see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]), and Hadamard type nonlinear FDEs without constant coefficient (see [1,Chapter 13] and [37][38][39][40][41][42][43]). However, the development of a related theory for Hadamard type nonlinear FDEs with constant coefficient is still in its infancy.…”

Nonlocal Cauchy problems for a class of implicit impulsive fractional relaxation differential systems

“…The corresponding fractional order differential equations model has been considered as an alternative model to integer order differential equations. For more background and the recent development of theory analysis for fractional differential equations as well B JinRong Wang wjr9668@126.com Yuruo Zhang yrzhangmath@126.com as control problems governed by fractional order systems, one can see [7][8][9][10][11][12][13][14][15][16][17][18][19] and etc. It seems that Bai and Fang [20] initially study nonlinear fractional differential systems.…”

Maximum principle for Hadamard fractional differential equations involving fractional Laplace operator

“…In 1892, Hadamard introduced Hadamard fractional derivative, which involved arbitrary exponent's logarithmic function. As for the related research of this topic, readers refer to the previous studies . However, in the existing literature, the Hadamard fractional extremum principle is rarely considered.…”

“…As for the related research of this topic, readers refer to the previous studies. [16][17][18][19][20][21][22][23][24] However, in the existing literature, the Hadamard fractional extremum principle is rarely considered. We recall that the papers mentioned above do not involve the fractional Laplace operator.…”