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Abstract
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By using the Caputo type and the Riemann-Liouville type fractional $q$-derivative, we investigate the existence of solutions for a multi-term pointwise defined fractional $q$-integro-differential equation $$D_q^{\alpha} u(t)= \omega \big(t, u(t), u'(t), D_q^{\beta_1} u(t), I_q^{\beta_2} u(t) \big)$$ with some boundary value conditions. In fact, we give some results by considering different conditions and using some classical fixed point techniques and the Lebesgue dominated convergence theorem.
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