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Existence of solutions to fractional order ordinary and delay differential equations and applications. (English) Zbl 1211.34096
Summary: We discuss the existence and uniqueness of solutions to fractional order ordinary and delay differential equations. We apply our results to single species model of Lotka Volterra type. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First, we use Banach contraction principle and then Krasnosel’skii’s fixed point theorem to show the existence and uniqueness of the solution under certain conditions. Moreover, we prove that the solution can be extended to the maximal interval of existence.
MSC:
34K37Functional-differential equations with fractional derivatives
34A08Fractional differential equations
47N20Applications of operator theory to differential and integral equations