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arXiv · 2404.09328

Existence and regularity results for space-time fractional integro-differential equation of Kirchhoff type with memory

Lalit Kumar·Sivaji Ganesh Sista·Konijeti Sreenadh
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Abstract

This paper analyses a Kirchhoff type quasilinear space-time fractional integro-differential equation with memory $(\mathcal{K}^{s}_{\alpha})$. Various a priori bounds are derived in different norms on the solution of the considered equation. Utilizing these a priori bounds, existence and uniqueness of the weak solution to the proposed model are proved. Furthermore, regularity results on the solution of $(\mathcal{K}^{s}_{\alpha})$ are established. The contribution made in this work provides a framework for further investigation of such types of partial integro-differential equation $(\mathcal{K}^{s}_{\alpha})$.

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Lalit Kumar, Sivaji Ganesh Sista, Konijeti Sreenadh. 2024-04-14. Existence and regularity results for space-time fractional integro-differential equation of Kirchhoff type with memory. https://arxiv.org/abs/2404.09328

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