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Mcheik‎, Salam, Shivanian, Elyas, El Seblani, Youssef. (1404). Existence and Uniqueness of High-Order Caputo Fractional Boundary Value Problems under General Non-Local Multi-Point Conditions‎: ‎Analytical and Semi-Analytical Approaches. فصلنامه علمی زیست فناوری گیاهان زراعی, 10(2), 153-184. doi: 10.30473/coam.2025.74523.1309
Salam Mcheik‎; Elyas Shivanian; Youssef El Seblani. "Existence and Uniqueness of High-Order Caputo Fractional Boundary Value Problems under General Non-Local Multi-Point Conditions‎: ‎Analytical and Semi-Analytical Approaches". فصلنامه علمی زیست فناوری گیاهان زراعی, 10, 2, 1404, 153-184. doi: 10.30473/coam.2025.74523.1309
Mcheik‎, Salam, Shivanian, Elyas, El Seblani, Youssef. (1404). 'Existence and Uniqueness of High-Order Caputo Fractional Boundary Value Problems under General Non-Local Multi-Point Conditions‎: ‎Analytical and Semi-Analytical Approaches', فصلنامه علمی زیست فناوری گیاهان زراعی, 10(2), pp. 153-184. doi: 10.30473/coam.2025.74523.1309
Mcheik‎, Salam, Shivanian, Elyas, El Seblani, Youssef. Existence and Uniqueness of High-Order Caputo Fractional Boundary Value Problems under General Non-Local Multi-Point Conditions‎: ‎Analytical and Semi-Analytical Approaches. فصلنامه علمی زیست فناوری گیاهان زراعی, 1404; 10(2): 153-184. doi: 10.30473/coam.2025.74523.1309

Existence and Uniqueness of High-Order Caputo Fractional Boundary Value Problems under General Non-Local Multi-Point Conditions‎: ‎Analytical and Semi-Analytical Approaches

Control and Optimization in Applied Mathematics
مقاله 6، دوره 10، شماره 2 - شماره پیاپی 20، مهر 2025، صفحه 153-184    اصل مقاله (617.35 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2025.74523.1309
نویسندگان
Salam Mcheik‎1؛ Elyas Shivanian* 1؛ Youssef El Seblani2
1Department of Applied Mathematics‎, ‎Imam Khomeini International University‎, ‎Qazvin‎, ‎34149-16818‎, ‎Iran.
2Khawarizmi Laboratory of Mathematics and Applications (KALMA)‎, ‎Faculty of Science, ‎Lebanese University, ‎Hadith-Beirut, ‎Lebanon.
چکیده
In this paper‎, ‎we investigate the existence and uniqueness of solutions for a high-order boundary value problem involving non-integer derivatives‎, ‎specifically utilizing the Caputo fractional derivative‎. ‎The problem is subject to non-local boundary conditions‎. ‎To tackle this‎, ‎we introduce the fractional Green's function as an analytical tool‎. ‎The Banach contraction fixed-point theorem serves as the fundamental method to establish our main results‎. ‎To support the theoretical findings‎, ‎we provide illustrative examples‎. ‎Furthermore‎, ‎we develop a numerical semi-analytical approach to approximate the unique solution with the desired accuracy‎.

تازه های تحقیق
  • Proved existence and uniqueness for a broad class of high-order boundary value problems (BVPs) involving Caputo fractional derivatives.
  • Introduced a nonlocal-capable fractional Green’s function as a core analytical tool.
  • Applied a fixed-point framework in well-posed function spaces.
  • Provided explicit and verifiable sufficient solvability conditions.
  • Developed a flexible, semi-analytical numerical scheme with proven convergence properties.
  • Demonstrated high-precision numerical convergence and stability.
  • Presented illustrative cases that validate the theory and show robustness to variations in ξ, boundary weights, and nonlinearity strength.
  • Supplied error bounds for the semi-analytical approximations and cross-validation with high-precision solvers.
  • Offered practical guidance for implementation in scientific computing workflows.
  • Expanded applicability to applied sciences and engineering domains.
کلیدواژه‌ها
Caputo fractional derivatives‎؛ ‎High-order boundary value problems‎؛ ‎Nonlocal boundary conditions‎؛ ‎Fractional Green’s function‎؛ ‎Fixed point theory
مراجع

[1] Adam, J.A. (1986). “A simplified mathematical model of tumor growth”, Mathematical Biosciences, 81(2), 229-244, doi:https://doi.org/10.1016/0025-5564(86)90119-7.

[2] Adam, J.A., Maggelakis, S. (1989). “Mathematical models of tumor growth. IV. Effects of a necrotic core”, Mathematical Biosciences, 97(1), 121-136. doi:https://doi.org/10.1016/0025-5564(89)90045-X.

[3] AhmadSoltani, L. (2022). “Two-point nonlocal nonlinear fractional boundary value problem with Caputo derivative: Analysis and numerical solution”, Nonlinear Engineering, 11(1), 71-79, doi:http://dx.doi.org/10.1515/nleng-2022-0009.

[4] Ali, A., Islam, S., Khan, M.R., Rasheed, S., Allehiany, F.M., Baili, J., Khan, M.A., Ahmad, H. (2022). “Dynamics of a fractional order Zika virus model with mutant”, Alexandria Engineering Journal, 61(6), 4821-4836, doi:https://doi.org/10.1016/j.aej.2021.10.031.

[5] Asaithambi, N., Garner, J. (1989). “Pointwise solution bounds for a class of singular diffusion problems in physiology”, Applied Mathematics and Computation, 30(3), 215-222, doi:https://doi.org/10.1016/0096-3003(89)90053-2.

[6] Bouteraa, N., Inc, M., Hashemi, M., Benaicha, S. (2022). “Study on the existence and nonexistence of solutions for a class of nonlinear Erdélyi-Kober type fractional differential equation on unbounded domain”, Journal of Geometry and Physics, 178, 104546, doi:https://doi.org/10.1016/j.geomphys.2022.104546.

[7] Burton, A.C. (1966). “Rate of growth of solid tumours as a problem of diffusion”, Growth, 30(2), 157-176.

[8] Delkhosh, M., Parand, K. (2021). “A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations”, Numerical Algorithms, 88, 729–766, doi:https://doi.org/10.1007/s11075-020-01055-9.

[9] Duggan, R.C., Goodman, A. (1986). “Pointwise bounds for the heat conduction model of the human head”, Bulletin of Mathematical Biology, 48(2), 229-236, doi:https://doi.org/10.1007/BF02460025.

[10] Flesch, U. (1975). “The distribution of heat sources in the human head: A theoretical consideration”, Journal of Theoretical Biology, 54(2), 285-287, doi:10.1016/S0022-5193(75)80164-1.

[11] Gray, B.F. (1980). “The distribution of heat sources in the human head—theoretical considerations”, Journal of Theoretical Biology, 82(3), 473-476, doi:https://doi.org/10.1016/0022-5193(80)90250-7.

[12] Hajimohammadi, Z., Baharifard, F., Ghodsi, A., Parand, K. (2021). “Fractional Chebyshev deep neural network (FDNN) for solving differential models”, Chaos, Solitons & Fractals, 153, 111530,  doi:https://doi.org/10.1016/j.chaos.2021.111530.

[13] Hashemi, M., Inc., M., Bayram, M. (2019). “Symmetry properties and exact solutions of the time fractional Kolmogorov-Petrouskii-Piskunov equation”, Revista Mexicana de Fisica, 65(5), 529-535, doi:https://doi.org/10.31349/revmexfis.65.529.

[14] Hosseinzadeh, N., Shivanian, E., Fairooz, M.Z., Chegini, T.G. (2025). “A robust RBF-FD technique combined with polynomial enhancements for valuing European options in jump-diffusion frameworks”, International Journal of Dynamics and Control, 13(6), 212, doi:https://doi.org/10.1007/s40435-025-01722-6.

[15] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. (2006). “Theory and applications of fractional differential equations”, Volume 204, Elsevier Science, Amsterdam, doi:https://www.sciencedirect.com/bookseries/north-holland-mathematics-studies/vol/204/suppl/C.

[16] Klages, R., Radons, G., Sokolov, I.M. (eds.) (2008). “Anomalous transport: Foundations and applications”, Wiley-VCH, doi:https://doi.org/10.1007/s10955-009-9713-5.

[17] Kubo, R. (1966). “The fluctuation-dissipation theorem”, Reports on Progress in Physics, 29(1), 255, doi:https://doi.org/10.1088/0034-4885/29/1/306.

[18] Kubo, R., Toda, M., Hashitsume, N. (2012). “Statistical physics II: Nonequilibrium statistical mechanics”, Springer Science & Business Media, Berlin, Heidelberg, doi:https://doi.org/10.1007/978-3-642-58244-8.

[19] Lakshmikantham, V., Bainov, D.D., Simeonov, P.S. (1989). “Theory of impulsive differential equations”, World Scientific, Singapore, doi:https://doi.org/10.1142/0906.

20] Li, X.P., Gul, N., Khan, M.A., Bilal, R., Ali, A., Alshahrani, M.Y., Muhammad, T., Islam, S. (2021). “A new Hepatitis B model in light of asymptomatic carriers and vaccination study through Atangana–Baleanu derivative”, Results in Physics, 29, 104603, doi:https://doi.org/10.1016/j.rinp.2021.104603.

[21] Magin, R.L. (2006). “Fractional calculus in bioengineering”, Begell House Publishers, doi:http://dx.doi.org/10.1615/critrevbiomedeng.v32.i1.10.

[22] McElwain, D.L.S. (1978). “A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics”, Journal of Theoretical Biology, 71(2), 255-263, doi:https://doi.org/10.1016/0022-5193(78)90270-9.

[23] Mehmood, N., Ahmad, N. (2020). “Existence results for fractional order boundary value problem with nonlocal non-separated type multi-point integral boundary conditions”, AIMS Mathematics, 5(1), 385-398, doi:https://doi.org/10.3934/math.2020026.

[24] Mohamed I.A. (2022). “Existence and uniqueness results for Riemann-Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations”, Asian-European Journal of Mathematics, 15(8), doi:http://dx.doi.org/10.1142/S1793557122501558.

[25] Parand, K., Aghaei, A., Jani, M., Ghodsi, A. (2021). “Parallel LS-SVM for the numerical simulation of fractional Volterra’s population model”, Alexandria Engineering Journal, 60(6), 5637-5647, doi:https://doi.org/10.1016/j.aej.2021.04.034.

[26] Plotnikov, A.V., Komleva, T.A., Molchanyuk, I.V. (2018). “Existence and uniqueness theorem for set-valued Volterra-Hammerstein integral equations”, Asian-European Journal of Mathematics, 11(03), 1850036, doi:https://doi.org/10.1142/S1793557118500365.

[27] Przeradzki, B., Stanczy, R. (2001). “Solvability of a multi-point boundary value problem at resonance”, Journal of Mathematical Analysis and Applications, 264(2), 253-261, doi:http://doi.org/10.1006/jmaa.2001.7616.

[28] Rao, S.N., Alesemi, M. (2019). “On a coupled system of fractional differential equations with nonlocal non-separated boundary conditions”. Advances in Difference Equations, 97, doi:https://doi.org/10.1186/s13662-019-2035-2.

[29] Refice, A., Inc., M., Hashemi, M., Souid, M.S. (2022). “Boundary value problem of Riemann-Liouville fractional differential equations in the variable exponent Lebesgue spaces Lp(.)”, Journal of Geometry and Physics, 178, 104554, doi:http://doi.org/10.1016/j.geomphys.2022.104554.

[30] Rehman, M., Khan, R.A. (2010). “Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations”, Applied Mathematics Letters, 23(9), 1038-1044, doi:https://doi.org/10.1016/ j.aml.2010.04.033.

[31] Shivanian, E., Jafarabadi, A., Chegini, T.G., Dinmohammadi, A. (2024). “Analysis of a time-dependent source function for the heat equation with nonlocal boundary conditions through a local meshless procedure”, Computational and Applied Mathematics, 43(1), 82, doi:http://doi.org/10.1007/s40314-025-03246-3.

[32] Shivanian, E., Hajimohammadi, Z., Baharifard, F., Parand, K., Kazemi, R. (2022). “A novel learning approach for different profile shapes of convecting–radiating fins based on shifted Gegenbauer LSSVM”, New Mathematics and Natural Computation, 18(3), 679-699, doi:http://doi.org/10.1142/S1793005723500060.

[33] Smirnov, S. (2019). “Green’s function and existence of solutions for a third-order three-point boundary value problem”, Mathematical Modelling and Analysis, 24(2), 171-178, doi:https://doi.org/10.3846/mma.2019.012.

[34] Sweilam, N.H., Khader, M.M., Al-Bar, R.F. (2007). “Numerical studies for a multi-order fractional differential equation”, Physics Letters A, 371(1-2), 26-33, doi:https://doi.org/10.1016/j.physleta.2007.06.016.

[35] Vinothkumar, C., Deiveegan, A., Nieto, J.J., Prakash, P. (2021). “Similarity solutions of fractional parabolic boundary value problems with uncertainty”, Communications in Nonlinear Science and Numerical Simulation, 102, 105926, doi:https://doi.org/10.1016/j.cnsns.2021.105926.

[36] Xu, Y.J., Bilal, M., Al-Mdallal, Q., Khan, M.A., Muhammad, T. (2021). “Gyrotactic microorganism flow of Maxwell nanofluid between two parallel plates”, Scientific Reports, 11(1), 15142, doi:https://doi.org/10.1038/s41598-021-94543-4.

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