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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
مراجع
  • [1]  T. Abdeljawad1 and M. E. Samei, Applying quantum calculus for the existence of solution of q-integro-differential equations with three criteria, Discrete & Continuous Dynamical Systems Series S, 14(10) (2021), 3351–3386.
  • [2]  N. Adjimi, A. Boutiara, M. E. Samei, et al., On solutions of a hybrid generalized Caputo-type problem via the noncompactness measure in the generalized version of Darbo’s criterion, J Inequal Appl 2023, 34 (2023).
  • [3]  Y. Adjabi, M. E. Samei, M. M. Matar, and J. Alzabut, Langevin differential equation in frame of ordinary and Hadamard fractional derivatives under three point boundary conditions, AIMS Mathematics, 6(3) (2021), 2796–2843.
  • [4]  Y. Allaoui, S. Melliani, A. EL Allaoui, and K. Hilal, Coupled System of Mixed Hybrid Fractional Differential Equations: Linear Perturbations of First and Second Type, In Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization, (2022), pp. 446–457.
  • [5]  P. Amiri and M. E. Samei, Existence of Urysohn and Atangana-Baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators, Chaos, Solitons & Fractals, 165(2) (2022), 112822.
  • [6]  Z. Baitiche, C. Derbazi, J. Alzabut, M. E. Samei, M. K. A. Kaabar, and Z. Siri, Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions, Fractal and Fractional, 5(3) (2021), 81.
  • [7]  M. Bouaouid, Mild Solutions of a Class of Conformable Fractional Differential Equations with Nonlocal Conditions. Acta Math. Appl. Sin. Engl. Ser. 39 (2023), 249–261.
  • [8]  A. Boutiara, M. Benbachir, J. Alzabut, and M. E. Samei, Monotone Iterative and Upper-Lower Solution Techniques for Solving the Nonlinear ψ-Caputo Fractional Boundary Value Problem, Fractal Fractional, 5(4) (2021), 194.
  • [9]  A. Boutiara, M. K. A. Kaabar, Z. Siri, M. E. Samei, and X. G. Yue, Investigation of a Generalized Proportional Langevin and Sturm-Liouville Fractional Differential Equations via Variable Coefficients and Anti-Periodic Boundary Conditions with a Control Theory Application arising from Complex Networks, Mathematical Problems in Engineering, (2022), 21.
  • [10]  Z. Cui and Z. Zhou, Existence of solutions for Caputo fractional delay differential equations with nonlocal and integral boundary conditions, Fixed Point Theory Algorithms Sci Eng 2023, 1 (2023).
  • [11]  C. Derbazi, Z. Baitiche, M. Benchohra, and J. R. Graef, Extremal solutions to a coupled system of nonlinear fractional differential equations with Caputo fractional derivatives, J. Math. Appl., 44 (2021), 19–34.
  • [12]  S. Etemad, I. Iqbal, M. E. Samei, et al., Some inequalities on multi-functions for applying fractional CaputoHadamard jerk inclusion system, Journal of Inequalities and Applications, 84 (2022).
  • [13]  V. Hedayati and M. E. Samei, Positive solutions of fractional differential equation with two pieces in chain interval and simultaneous Dirichlet boundary conditions, Bound Value Probl., 141 (2019).
  • [14]  M. Houas and M. E. Samei, Existence and Mittag-Leffler-Ulam-stability results for Duffing type problem involving sequential fractional derivatives,Int. J. Appl. Comput. Math 8, 185 (2022).
  • [15]  T. Kherraz, M. Benbachir, M. Lakrib, M. E. Samei, M. K. A. Kaabar, and S. A. Bhanotar, Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals, Chaos Solitons & Fractals. 166(1) (2023), 113007.
  • [16]  A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North Holland Mathematics Studies, Elsevier Science B. V., Amsterdam, 204 (2006).
  • [17]  D. Kumar and D. Baleanu, Fractional calculus and its applications in physics Frontiers in Physics, 7(6) 81 (2019).
  • [18]  M. Rahaman, S. P. Mondal, A. El Allaoui, S. Alam, and A. Ahmadian, and S. Salahshour, Solution strategy for fuzzy fractional order linear homogeneous differential equation by Caputo-H differentiability and its application in fuzzy EOQ model. Advances in Fuzzy Integral and Differential Equations, (2022), 143–157.
  • [19]  S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, (Yverdon: Gordon and Breach), 1993.
  • [20]  E. Shivanian and A. Dinmohammadi, On the solution of a nonlinear fractional integro-differential equation with non-local boundary condition, International Journal of Nonlinear Analysis and Applications, (2023), 1–12.
  • [21]  M. E. Samei, L. Karimi, and M. K. A. Kaabar, To investigate a class of multi-singular pointwise defined fractional integro-differential equation with applications. AIMS Mathematics, 7(5) (2022), 7781–7816.
  • [22]  M. E. Samei, H. Zanganeh, and S. M. Aydogan, Investigation of a Class of the Singular Fractional Integrodifferential Quantum Equations with Multi-Step Methods, Journal of Mathematical Extension, 15 (2021), 1–54.
  • [23]  M. Sangi and S. Saiedinezhad, and M. B. Ghaemi, A System of High-Order Fractional Differential Equations with Integral Boundary Conditions, J Nonlinear Math Phys, 30 (2023), 699–718.
  • [24]  H. Sun, A. Chang, Y. Zhang, and W. Chen, A review on variable-order fractional differential equations: Mathematical foundations, physical models, numerical methods and applications, Fractional Calculus and Applied Analysis, 22(1) (2019), 27–59.
  • [25]  J. A. Tenreiro Machado, Handbook of Fractional Calculus with Applications (Berlin-Boston: Walter de Gruyter GmbH), (2019).
  • [26]  J. Wang, Y. Zhou, and W. Wei1, Study in fractional differential equations by means of topological degree methods, Numer. Funct. Anal. Optim., 33(2) (2012), 216–238.
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تعداد مشاهده مقاله: 365
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