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Shivanian, Elyas, Fatahi, Hedayat. (1402). To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition. سامانه مدیریت نشریات علمی, 11(2), 332-344. doi: 10.22034/cmde.2022.51628.2153
Elyas Shivanian; Hedayat Fatahi. "To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition". سامانه مدیریت نشریات علمی, 11, 2, 1402, 332-344. doi: 10.22034/cmde.2022.51628.2153
Shivanian, Elyas, Fatahi, Hedayat. (1402). 'To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition', سامانه مدیریت نشریات علمی, 11(2), pp. 332-344. doi: 10.22034/cmde.2022.51628.2153
Shivanian, Elyas, Fatahi, Hedayat. To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition. سامانه مدیریت نشریات علمی, 1402; 11(2): 332-344. doi: 10.22034/cmde.2022.51628.2153

To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition

Computational Methods for Differential Equations
مقاله 10، دوره 11، شماره 2، تیر 2023، صفحه 332-344    اصل مقاله (346.93 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.51628.2153
نویسندگان
Elyas Shivanian* 1؛ Hedayat Fatahi2
1Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.
2Department of Mathematics, Baneh Branch, Islamic Azad University, Baneh, Iran.
چکیده
In this paper, we prove the existence and uniqueness of the solutions for a non-integer high order boundary value problem which is subject to the Caputo fractional derivative. The boundary condition is a non-local type. Analytically, we introduce the fractional Green’s function. The main principle applied to simulate our results is the Banach contraction fixed point theorem. We deduce this paper by presenting some illustrative examples. Furthermore, it is presented a numerical based semi-analytical technique to approximate the unique solution to the desired order of precision. 
کلیدواژه‌ها
High order fractional differential equation؛ Caputo fractional derivative؛ Boundary value problem؛ Existence and uniqueness؛ Fixed point theorem
مراجع
  • [1] M. I. Abbas, Existence and uniqueness results for riemann–stieltjes integral boundary value problems of nonlinear implicit hadamard fractional differential equations, Asian-European Journal of Mathematics, (2021), 2250155.
  • [2] J. A. Adam, A mathematical model of tumor growth. ii. effects of geometry and spatial nonuniformity on stability, Mathematical Biosciences, 86(2) (1987), 183–211.
  • [3] J. A. Adam, A simplified mathematical model of tumor growth, Mathematical biosciences, 81(2) (1986), 229–244.
  • [4] J. A. Adam and S. Maggelakis, Mathematical models of tumor growth. iv. effects of a necrotic core, Mathematical biosciences, 97(1) (1989), 121–136.
  • [5] R. P. Agarwal, M. Bohner, and V. B. Shakhmurov, Linear and nonlinear nonlocal boundary value problems for differential-operator equations, Applicable Analysis, 85(6-7) (2006), 701–716.
  • [6] L. AhmadSoltani, Two-point nonlocal nonlinear fractional boundary value problem with caputo derivative: Analysis and numerical solution, Nonlinear Engineering, 11(1) (2022), 71–79.
  • [7] N. Asaithambi and J. Garner, Pointwise solution bounds for a class of singular diffusion problems in physiology, Applied Mathematics and Computation, 30(3) (1989), 215–222.
  • [8] N. Bouteraa, M. Inc, M. Hashemi, and S. Benaicha, Study on the existence and nonexistence of solutions for a class of nonlinear erdelyi-kober type fractional differential equation on unbounded domain, Journal of Geometry and Physics, (2022) 104546.
  • [9] A. C. Burton, Rate of growth of solid tumours as a problem of diffusion, Growth, 30(2) (1966), 157–176.
  • [10] M. Delkhosh and K. Parand, A new computational method based on fractional lagrange functions to solve multi- term fractional differential equations, Numerical Algorithms, 88(2) (2021), 729–766.
  • [11] A. Dinmohammadi, A. Razani, and E. Shivanian, Analytical solution to the nonlinear singular boundary value problem arising in biology, Boundary Value Problems, 2017(1) (2017), 1–9.
  • [12] A. Dinmohammadi, E. Shivanian, and A. Razani, Existence and uniqueness of solutions for a class of singular nonlinear two-point boundary value problems with sign-changing nonlinear terms, Numerical Functional Analysis and Optimization, 38(3) (2017), 344–359.
  • [13] R. Duggan and A. Goodman, Pointwise bounds for a nonlinear heat conduction model of the human head, Bulletin of mathematical biology, 48(2) (1986), 229–236.
  • [14] J. R. Graef and J. Webb, Third order boundary value problems with nonlocal boundary conditions, Nonlinear Analysis: Theory, Methods & Applications, 71(5-6), (2009) 1542–1551.
  • [15] U. Flesch, The distribution of heat sources in the human head: a theoretical consideration, Journal of theoretical biology, 54(2) (1975), 285–287.
  • [16] B. Gray, The distribution of heat sources in the human head—theoretical considerations, Journal of theoretical biology, 82(3) (1980), 473–476.
  • [17] H. Greenspan, Models for the growth of a solid tumor by diffusion, Studies in Applied Mathematics, 51(4) (1972), 317–340.
  • [18] Z. Hajimohammadi, F. Baharifard, A. Ghodsi, and K. Parand, Fractional chebyshev deep neural network (fcdnn) for solving differential models, Chaos, Solitons & Fractals, 153 (2021), 111530.
  • [19] F. Haq, K. Shah, G. Rahman, and M. Shahzad, Coupled system of non local boundary value problems of nonlinear fractional order differential equations, J. Math. Anal, 8(2) (2017), 51–63.
  • [20] M. Hashemi, M. Inc, and M. Bayram, Symmetry properties and exact solutions of the time fractional kolmogorov- petrovskii-piskunov equation, Revista mexicana de fısica, 65(5) (2019), 529–535.
  • [21] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 204 (2006)
  • [22] R. Klages, G. Radons, and I. M. Sokolov, Anomalous transport, Wiley Online Library, 2008.
  • [23] R. Kubo, The fluctuation-dissipation theorem, Reports on progress in physics, 29(1) (1966), 255.
  • [24] R. Kubo, M. Toda, and N. Hashitsume, Statistical physics II: nonequilibrium statistical mechanics, Vol. 31, Springer Science & Business Media, 2012.
  • [25] R. Ma, A survey on nonlocal boundary value problems, Appl. Math. E-Notes, 7 (2007), 257–279.
  • [26] R. L. Magin, Fractional calculus in bioengineering, Begell House Redding, 2, 2006.
  • [27] D. McElwain, A re-examination of oxygen diffusion in a spherical cell with michaelis-menten oxygen uptake kinetics, Journal of Theoretical Biology, 71(2) (1978), 255–263.
  • [28] N. Mehmood and N. Ahmad, Existence results for fractional order boundary value problem with nonlocal non- separated type multi-point integral boundary conditions, AIMS Math 5 (2019), 385–398.
  • [29] K. Parand, A. Aghaei, M. Jani, and A. Ghodsi, Parallel ls-svm for the numerical simulation of fractional volterra’s population model, Alexandria Engineering Journal, 60(6) (2021), 5637–5647.
  • [30] A. V. Plotnikov, T. A. Komleva, and I. V. Molchanyuk, Existence and uniqueness theorem for set-valued volterra- hammerstein integral equations, Asian-European Journal of Mathematics, 11(03) (2018), 1850036.
  • [31] B. Przeradzki and R. Stanczy, Solvability of a multi-point boundary value problem at resonance, Journal of math- ematical analysis and applications, 264(2) (2001), 253–261.
  • [32] A. Refice, M. Inc, M. S. Hashemi, and M. S. Souid, Boundary value problem of riemann-liouville fractional differential equations in the variable exponent lebesgue spaces lp(.), Journal of Geometry and Physics, 178 (2022), 104554.
  • [33] M. Rehman and R. A. Khan, Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations, Applied Mathematics Letters, 23(9) (2010), 1038– 1044.
  • [34] E. Shivanian, Z. Hajimohammadi, F. Baharifard, K. Parand, and R. Kazemi, A novel learning approach for different profile shapes of convecting–radiating fins based on shifted gegenbauer lssvm, New Mathematics and Natural Computation, (2022), 1–21.
  • [35] S. Smirnov, Green’s function and existence of solutions for a third-order three-point boundary value problem, Mathematical Modelling and Analysis, 24(2) (2019), 171–178.
  • [36] C. Vinothkumar, A. Deiveegan, J. Nieto, P. Prakash, Similarity solutions of fractional parabolic boundary value problems with uncertainty, Communications in Nonlinear Science and Numerical Simulation, 102 (2021), 105926.
  • [37] X. Zhang and L. Liu, Positive solutions of fourth-order multi-point boundary value problems with bending term, Applied mathematics and computation, 194(2) (2007), 321–332.
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