M. Caponi, P. Pucci:
 Existence theorems for entire solutions of stationary Kirchhoff fractional p-Laplacian equations
Ann. Mat. Pura Appl. Vol. 195, p. 2099-2129, 2016

M. Caponi:
Linear Hyperbolic Systems in Domains with Growing Cracks
Milan J. Math. Vol. 85, p. 149-185, 2017

M. Caponi:
On some mathematical problems in fracture dynamics
(Ph.D. Thesis) 2019

M. Caponi:
Existence of solutions to a phase-field model of dynamic fracture with a  crack-dependent dissipation
NoDEA Nonlinear Differential Equations Appl. 2020

M. Caponi, F. Sapio:
A dynamic model for viscoelastic materials with prescribed growing  cracks
Annali di Matematica Pura ed Applicata (1923 -) Vol. 199, p. 1263-1292, 2020

M. Caponi, I. Lucardesi, E. Tasso:
Energy-dissipation balance of a smooth moving crack
Journal of Mathematical Analysis and Applications 2020

M. Caponi, F. Sapio:
An existence result for the fractional Kelvin-Voigt's model on time-dependent cracked domains
Journal of Evolution Equations 2021

N. Cangiotti, M. Caponi, A. Maione, E. Vitillaro:
Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators
Milan Journal of Mathematics Vol. 91, N. 2, p. 375-403, 2023

N. Cangiotti, M. Caponi, A. Maione, E. Vitillaro:
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators
Fractional Calculus and Applied Analysis 2024

M. Caponi, A. Carbotti, F. Sapio:
The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture
Journal of Evolution Equations p. 24, 2024

M. Caponi, V. Crismale:
A rate-independent model for geomaterials under compression coupling  strain gradient plasticity and damage
ESAIM Control Optim. Calc. Var. Vol. 31, p. Article 14 (49 pp.), 2025

S. Almi, M. Caponi, M. Friedrich, F. Solombrino:
Riesz fractional gradient functionals defined on partitions: nonlocal-to-local variational limits
(Preprint) http://arxiv.org/abs/2510.04881 p. 30, 2025

M. Caponi, A. Carbotti, A. Maione:
$H$-compactness for nonlocal linear operators in fractional divergence form
Calculus of Variations and Partial Differential Equations Vol. 64, N. 9, p. 36, 2025

S. Almi, M. Caponi, M. Friedrich, F. Solombrino:
Geometric rigidity on Sobolev spaces with variable exponent and applications
Nonlinear Differential Equations and Applications 2025

S. Almi, M. Caponi, M. Friedrich, F. Solombrino:
A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations
Mathematische Annalen 2025

M. Caponi:
A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces
To appear as book chapter in "New Frontiers in Homogenization and Fractional Calculus" (Accepted Paper) http://arxiv.org/abs/2509.11734 p. 19, 2026

G. C. Brusca, M. Caponi, A. Carbotti, A. Maione, F. Paronetto:
$H$-convergence and $\Gamma$-convergence in the Riesz fractional setting: the nonlinear case
(Submitted Paper) http://arxiv.org/abs/2607.06725 p. 34, 2026