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

نویسندگان
Melliani, Said ID 1
El Khalfi, Hamid ID 2
El Allaoui, Abdelati ID 3
Allaoui, Youssef ID 4

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

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

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

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

doi
10.22034/cmde.2023.56512.2363
چکیده

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.

کلیدواژه‌ها
Arzel\`a-Ascoli's theorem, Caputo fractional derivative, Integro-differential equation, Nonlinear boundary conditions