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

S. Almi, M. Caponi, M. Friedrich, F. Solombrino:
Geometric rigidity on Sobolev spaces with variable exponent and applications
Nonlinear Differential Equations and Applications (Accepted Paper) http://arxiv.org/abs/2305.00740 2023

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

M. Caponi, A. Carbotti, A. Maione:
$H$-compactness for nonlocal linear operators in fractional divergence form
(Submitted Paper) http://arxiv.org/abs/2408.10984v2 2024

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

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