Uniqueness of solution of multi-term fractional order Volterra Integro-differential equations with convergence analysis

Résumé

This paper focused on multi-term fractional order Volterra integro-differential equations. The multi-term fractional order derivative part of the multi-term fractional order Volterra integrodifferential equations is converted into its equivalent integral equation then Banach contraction principle is utilised in the establishment of the uniqueness of solution for multi-term fractional order Volterra integro-differential equations under some condition. Furthermore, the convergence of the solution is also studied and proved. Some examples were considered to test the applicability of the proposed uniqueness theorem for the solution of multi-term fractional order Volterra integro-differential equations.