Existence and uniqueness of mild and strong solutions of nonlinear fractional integrodifferential equation

A. D. Nagargoje, V. C. Borkar, V. D. Mathpati

Abstract


In this paper, we will discuss some results on the existence and uniqueness of mild and strong solution of initial value problem of fractional order subjected to non-local conditions, by using the Banach fixed point theorem and the theory of strongly continuous cosine family under Caputo sense. Furthermore, we also prove that solution of Nonlinear Fractional Volterra Integrodifferential Equations and Nonlinear Fractional Mixed Integrodifferential Equations With Nonlocal Conditions is unique. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

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Published: 2022-01-24

How to Cite this Article:

A. D. Nagargoje, V. C. Borkar, V. D. Mathpati, Existence and uniqueness of mild and strong solutions of nonlinear fractional integrodifferential equation, J. Math. Comput. Sci., 12 (2022), Article ID 67

Copyright © 2022 A. D. Nagargoje, V. C. Borkar, V. D. Mathpati. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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