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Discontinuity, Nonlinearity, and Complexity 13(1) (2024) 189--202 | DOI:10.5890/DNC.2024.03.014

K. Kaliraj$^{1,}$, U. Aswini$^1$, C. Ravichandran$^2$, K. Logeswari$^2$, Kottakkaran Sooppy Nisar$^3$

$^1$ Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, Tamil Nadu, India

$ ^2$ Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, Tamil Nadu, India

$^3$ Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

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Abstract

In this work, we derived the existence of mild solutions for fractional functional mixed integro-differential equations in Banach spaces. Standard fixed point techniques are used to obtained the results. Initially, we first formulate the definition of PC-mild solution and we prove the existence of solutions for the considered fractional system. Finally, we present an example to demonstrate the obtained theoretical results.

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