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

Abstract

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.

Topics & Concepts