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El Allaoui, Abdelati, Allaoui, Youssef, Melliani, Said, El Khalfi, Hamid. (1403). Upper and lower solutions for fractional integro-differential equation of higher-order and with nonlinear boundary conditions. سامانه مدیریت نشریات علمی, 12(3), 438-453. doi: 10.22034/cmde.2023.56512.2363
Abdelati El Allaoui; Youssef Allaoui; Said Melliani; Hamid El Khalfi. "Upper and lower solutions for fractional integro-differential equation of higher-order and with nonlinear boundary conditions". سامانه مدیریت نشریات علمی, 12, 3, 1403, 438-453. doi: 10.22034/cmde.2023.56512.2363
El Allaoui, Abdelati, Allaoui, Youssef, Melliani, Said, El Khalfi, Hamid. (1403). 'Upper and lower solutions for fractional integro-differential equation of higher-order and with nonlinear boundary conditions', سامانه مدیریت نشریات علمی, 12(3), pp. 438-453. doi: 10.22034/cmde.2023.56512.2363
El Allaoui, Abdelati, Allaoui, Youssef, Melliani, Said, El Khalfi, Hamid. Upper and lower solutions for fractional integro-differential equation of higher-order and with nonlinear boundary conditions. سامانه مدیریت نشریات علمی, 1403; 12(3): 438-453. doi: 10.22034/cmde.2023.56512.2363

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

Computational Methods for Differential Equations
مقاله 2، دوره 12، شماره 3، مهر 2024، صفحه 438-453    اصل مقاله (457.81 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.56512.2363
نویسندگان
Abdelati El Allaoui* 1؛ Youssef Allaoui2؛ Said Melliani2؛ Hamid El Khalfi3
1MISCOM, National School of Applied Sciences, Cadi Ayyad University, Marrakech, Morocco
2LMACS, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Beni Mellal, Morocco
3Lab. LMRI, FP of Khouribga, Sultan Moulay Slimane University, Morroco
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
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