@article{Hassan2026, 
author = {Taher S. Hassan and Ali Rezaiguia and Loredana Florentina Iambor and Ismoil Odinaev},
title = {Filippov-type existence theorems for    q-fractional differential inclusions with nonlinear    q-integral conditions in Banach spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4539-4556},
keywords = {Caputo fractional q-difference inclusion, fixed point theorems, integral boundary conditions},
url = {https://www.sciopen.com/article/10.3934/math.2026182},
doi = {10.3934/math.2026182},
abstract = {This study focused on boundary value problems involving fractional    q-difference inclusions subject to nonlinear    q-integral conditions:                                                       c                                    D                      q            ,                          γ                                                (                      ν                          (              ι              )                        −            h                          (                              ι                ,                ν                                  (                  ι                  )                                            )                                )                ∈        F                  (                      ι            ,            ν                          (              ι              )                                )                ,                ι        ∈                  [                      0            ,            ℓ                    ]                ,        1        <                  γ                ≤        2        ,                            ν                  (          0          )                −                  ν                      ′                                    (          0          )                =        a                  (          ι          )                          ∫                      0                                ℓ                                                G                                1                                    (                      τ            ,            ν                          (              τ              )                                )                          d                      q                          τ        ,                            ν                  (          ℓ          )                −                  ν                      ′                                    (          ℓ          )                =        b                  (          ι          )                          ∫                      0                                ℓ                                                G                                2                                    (                      τ            ,            ν                          (              τ              )                                )                          d                      q                          τ        .            By applying appropriate fixed point theorems, we established the existence of solutions to the problem considered. In addition, a Filippov-type result was provided. This work continued the study recently presented in [N. Allouch, J. R. Graef, S. Hamani, Boundary value problem for fractional    q-difference equations with integral conditions in Banach spaces, Fractal Fract., 6 (2022), 237].}
}