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Filippov-type existence theorems for q-fractional differential inclusions with nonlinear q-integral conditions in Banach spaces
AIMS Mathematics 2026, 11(2): 4539-4556
Published: 13 February 2026
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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 , ] , 1 < γ 2 , ν ( 0 ) ν ( 0 ) = a ( ι ) 0 G 1 ( τ , ν ( τ ) ) d q τ , ν ( ) ν ( ) = b ( ι ) 0 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].

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