APPLYING QUANTUM CALCULUS FOR THE EXISTENCE OF SOLUTION OF q-INTEGRO-DIFFERENTIAL EQUATIONS WITH THREE CRITERIA

摘要

Crisis intervention in natural disasters is significant to look atfrom many different slants. In the current study, we investigate the existenceof solutions for q-integro-differential equationD_q~α u(t) + w(t, u(t); u′(t),D_q~β u(t),∫_0~t f(r)u(r) dr,ψ(u(t))= 0,with three criteria and under some boundary conditions which therein we usethe concept of Caputo fractional q-derivative and fractional Riemann-Liouvilletype q-integral. New existence results are obtained by applying α-admissiblemap. Lastly, we present two examples illustrating the primary effects.