Applying quantum calculus for the existence of solution of <tex-math id="M1">q</tex-math>-integro-differential equations with three criteria

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 equationDqα u(t) + w(t , u(t), u'(t), Dqβ u(t), ∫₀ᵗ f(r) u(r) \, dr, φ(u(t)) ) = 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 α-admissible map. Lastly, we present two examples illustrating the primary effects.