This accessible monograph is devoted to a rapidly developing area on the research of
qualitative theory of fractional ordinary differential equations and evolution equations. It is …

In this paper we obtain the Hermite–Hadamard and Hermite–Hadamard–Fejér type
inequalities for fractional integrals which generalize the two familiar fractional integrals …

An analogous version of Hermite-Hadamard-Mercer's inequality has been established using
the Katugampola fractional integral operators. The result is the generalization of the …

The author (Bull. Math. Anal. App. 6 (4)(2014): 1-15), introduced a new fractional
derivative,\[{}^\rho\mathcal {D} _a^\alpha f (x)=\frac {\rho^{\alpha-n+ 1}}{\Gamma ({n …

This paper is concerned with a numerical method for solving generalized fractional
differential equation of Caputo–Katugampola derivative. A corresponding discretization …

In this paper we introduce a new fractional integral that generalizes six existing fractional
integrals, namely, Riemann-Liouville, Hadamard, Erd\'elyi-Kober, Katugampola, Weyl and …

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant
link between convexity and integral inequality. Due to the significance of these concepts, the …

Noninstantaneous impulsive inequalities via conformable fractional calculus | Journal of
Inequalities and Applications Skip to main content SpringerLink Account Menu Find a journal …

This research paper is about the existence and uniqueness of the coupled system of
nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary …

In this work we consider the higher order fractional differential equation with derivative
defined in the sense of Katugampola. We present some equivalent integral form of the …