Survey and new results on boundary-value problems of singular fractional differential equations with impulse effects

Abstract

Firstly we prove existence and uniqueness of solutions of Cauchy problems of linear fractional differential equations (LFDEs) with two variable coefficients involving Caputo fractional derivative, Riemann-Liouville derivative, Caputo type Hadamard derivative and Riemann-Liouville type Hadamard fractional derivatives with order q in [n-1,n) by using the iterative method.

Keywords

• Higher order singular fractional differential system
• impulsive boundary value problem
• Riemann-Liouville fractional derivative
• Caputo fractional derivative
• Riemann-Liouville type Hadamard
• fractional derivative
• Caputo type Hadamard fractional derivative
• fixed point theorem