A Gronwall inequality via the generalized proportional fractional derivative with applications

A generalized discrete fractional Gronwall inequality and its application on the uniqueness of solutions for nonlinear delay fractional difference system

(2018) Jehad Alzabut et al.   Applicable Analysis and Discrete Mathematics

Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives

(2018) Thabet Abdeljawad et al.   JOURNAL OF INEQUALITIES AND APPLICATIONS

On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative

(2018) Fahd Jarad et al.   CHAOS SOLITONS & FRACTALS

Lyapunov-type inequalities for fractional difference operators with discrete Mittag-Leffler kernel of order 2 < α < 5/2

(2017) Thabet Abdeljawad et al.   European Physical Journal-Special Topics

Generalized fractional derivatives generated by a class of local proportional derivatives

(2017) Fahd Jarad et al.   European Physical Journal-Special Topics

A generalized Lyapunov-type inequality in the frame of conformable derivatives

(2017) Thabet Abdeljawad et al.   Advances in Difference Equations

Fractional operators with exponential kernels and a Lyapunov type inequality

(2017) Thabet Abdeljawad   Advances in Difference Equations

New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model

(2016) Abdon Atangana et al.   Thermal Science

A generalized Gronwall inequality and its application to fractional neutral evolution inclusions

(2016) Zufeng Zhang et al.   JOURNAL OF INEQUALITIES AND APPLICATIONS

A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems

(2016) Thabet Abdeljawad et al.   JOURNAL OF INEQUALITIES AND APPLICATIONS

On conformable fractional calculus

(2015) Thabet Abdeljawad   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A new definition of fractional derivative

(2014) R. Khalil et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A discrete fractional Gronwall inequality

(2012) Rui A. C. Ferreira   PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY