Abstract
In this manuscript, exciting fixed point results for a pair of multivalued mappings justifying rational Gupta-Saxena type omega-contractions in the setting of extended b-metric-like spaces are established. The theoretical results have also been strengthened by some nontrivial examples. Finally, the theoretical results are used to study the existence of the solution of Fredholm integral equation which arises from the damped harmonic oscillator, to study initial value problem which arises from Newton's law of cooling and to study infinite systems of fractional ordinary differential equations (ODEs).