Convexity in terms of Caputo fractional derivatives
Abstract
The first criterion of convexity states that a differentiable function defined on an open interval is convex if and only if its first derivative is increasing. The second criterion of convexity states that a twice differential function is convex if and only if its second derivative is positive. In this work, by using a change of variable transforming the interval [a,t] into [0,1], we are able to get a new formulation of Caputo derivative. Then, we use this new version of Caputo derivative to investigate convexity and obtain generalizations to the first and second criteria of convexity depending on fractional orders 0<α<1 and 1<α<2, respectively. As a further application of the new representation of the Caputo derivative (Daα f)(x) of a function f defined on an interval [a,b] and of order $n-1<\alpha
Related
- Backward Homogeneous Heat Equation with Ψ-Caputo Time Derivative and Spectral Fractional Laplacian
- Extremal and uniqueness results for a singular p-Laplacian Caputo-Hadamard fractional equation involving parameter dependence
- A Comparative B-Spline Collocation Framework for the Caputo Time-Fractional Mobile–Immobile Transport Equation
- Existence, Uniqueness, and Continuous Dependence on Initial/Final Values for Liouville–Caputo Fractional Difference Equations
- Exact Analytic Solution for the Time-Fractional Hunter-Saxton Equation with Caputo derivative
BibTeX
@article{bouafia2026convexity,
title = {{Convexity in terms of Caputo fractional derivatives}},
author = {Mousaab Bouafia and Adnan Yassine and Thabet Abdeljawad},
journal = {RAIRO - Operations Research},
year = {2026},
month = sep,
doi = {10.1051/ro/2026080},
url = {https://hal.science/hal-05692615v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Convexity in terms of Caputo fractional derivatives
AU - Mousaab Bouafia
AU - Adnan Yassine
AU - Thabet Abdeljawad
PY - 2026
DA - 2026/09/11
JO - RAIRO - Operations Research
DO - 10.1051/ro/2026080
UR - https://hal.science/hal-05692615v1
AB - The first criterion of convexity states that a differentiable function defined on an open interval is convex if and only if its first derivative is increasing. The second criterion of convexity states that a twice differential function is convex if and only if its second derivative is positive. In this work, by using a change of variable transforming the interval [a,t] into [0,1], we are able to get a new formulation of Caputo derivative. Then, we use this new version of Caputo derivative to investigate convexity and obtain generalizations to the first and second criteria of convexity depending on fractional orders 0<α<1 and 1<α<2, respectively. As a further application of the new representation of the Caputo derivative (D_a^α f)(x) of a function f defined on an interval [a,b] and of order $n-1<\alpha
SN - 0399-0559
SN - 1290-3868
ER -