A solution to nonlinear Volterra integro-dynamic equations via fixed point theory. (English) Zbl 1499.45009
Summary: In this paper we discuss the existence and uniqueness of solutions of a certain type of nonlinear Volterra integro-dynamic equations on time scales. We investigate the problem in the setting of a complete \(b\)-metric space and apply a fixed point theorem with a contractive condition involving \(b\)-comparison function. We use the theorem to show the existence of a unique solution of some particular integro-dynamic equations.
MSC:
| 45D05 | Volterra integral equations |
| 26E70 | Real analysis on time scales or measure chains |
| 47N20 | Applications of operator theory to differential and integral equations |
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