Upper and lower solutions for fractional integro-differential equation of higher-order and with nonlinear boundary conditions

El Allaoui, Abdelati; Allaoui, Youssef; Melliani, Said; El Khalfi, Hamid

doi:10.22034/cmde.2023.56512.2363

Upper and lower solutions for fractional integro-differential equation of higher-order and with nonlinear boundary conditions

Document Type : Research Paper

Authors

¹ MISCOM, National School of Applied Sciences, Cadi Ayyad University, Marrakech, Morocco

² LMACS, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Beni Mellal, Morocco

³ Lab. LMRI, FP of Khouribga, Sultan Moulay Slimane University, Morroco

10.22034/cmde.2023.56512.2363

Abstract

This paper delves into the identification of upper and lower solutions for a high-order fractional integro-differential equation featuring non-linear boundary conditions. By introducing an order relation, we define these upper and lower solutions. Through a rigorous approach, we demonstrate the existence of these solutions as the limits of sequences derived from carefully selected problems, supported by the application of Arzel\`a-Ascoli's theorem. To illustrate the significance of our findings, we provide an illustrative example. This research contributes to a deeper understanding of solutions in the context of complex fractional integro-differential equations.

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