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چکیده
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Crisis intervention in natural disasters is significant to look at from many different slants. In the current study, we investigate the existence of solutions for $q$-integro-differential equation $$D_q^{\alpha} u(t) + w\left(t , u(t), u'(t), D_q^{\beta} u(t), \int_0^t f(r) u(r) \, {\mathrm d}r, \varphi(u(t)) \right) =0,$$ with three criteria and under some boundary conditions which therein we use the concept of Caputo fractional $q$-derivative and fractional Riemann-Liouville type $q$-integral. New existence results are obtained by applying $\alpha$-admissible map. Lastly, we present two examples illustrating the primary effects.
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