On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

Initial time difference quasilinearization for Caputo Fractional Differential Equations

Correspondence: [email protected]. tr Department of Statistics, Gaziosmanpasa University, Tasliciftlik Campus, 60250 Tokat, Turkey Abstract This paper deals with an application of the method of quasilinearization by not demanding the Hölder continuity assumption of functions involved and by choosing upper and lower solutions with initial time difference for nonlinear Caputo fractional different...

Right Caputo Fractional Landau Inequalities

Right Caputo fractional ∥·∥p-Landau type inequalities, p ∈ (1,∞] are obtained with applications on R−.

A monotonicity result for discrete fractional difference operators

In this note we demonstrate that if y(t) ≥ 0, for each t in the domain of t → y(t), and if, in addition, Δ0y(t) ≥ 0, for each t in the domain of t → Δ0y(t), with 1 < ν < 2, then it holds that y is an increasing function of t. This demonstrates that, in some sense, the positivity of the νth order fractional difference has a strong connection to the monotonicity of y. Furthermore, we provide a du...

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

On q–fractional derivatives of Riemann–Liouville and Caputo type

Abstract. Based on the fractional q–integral with the parametric lower limit of integration, we define fractional q–derivative of Riemann–Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we discuss properties of compositions of these operators. Mathematics Subject Classification: 33D60, 26A33 .