Basic Theory of Fractional Differential Equations

Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative

“…See, for example, the books [1,2,3,5,17,34] and references therein. Fractional differential equations arise naturally in various fields such as viscoelastic materials, polymer science, fractals, chaotic dynamics, nonlinear control, signal processing, bioengineering and chemical engineering, etc.…”

On the Oscillation of Impulsive Partial Fractional Differential Equations

“…The theories of fractional differential equations and their applications have been investigated extensively, we can find numerous applications in viscoelasticity, electrochemistry, control, porousmedia, electromagnetic, etc. see [1][2][3][4][5][6]. The oscillatory behavior of ordinary differential equations, partial differential equations and impulsive partial differential equations have been investigated by many papers in the past, see [7][8][9][10][11].…”

Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

“…Fractional differential equations can describe phenomena in fields such as control, porous media, electrochemistry, viscoelasticity, and electromagnetism [1][2][3][4] . Zhou and Peng 5,6 obtained the existence and uniqueness of local and global mild solutions for the time-fractional Navier-Stokes equations by using fixed point theory.…”