Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 6 Sayı: 4, 188 - 193, 31.12.2023

Serkan İlter

https://doi.org/10.33401/fujma.1333804

Öz

Kaynakça

  • [1] M. Abbas, A.A. Majid, A.I.M. Ismail and A. Rashid, The application of cubic trigonometric B-spline to the numerical solution of the hyperbolic problems, Appl. Math. Comput., 239 (2014), 74–88.
  • [2] J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, (1990).
  • [3] P. Bettiol and H. Frankowska, Regularity of solution maps of differential inclusions under state constraints, Set-Valued Var. Anal., 15(1) (2007), 21-45.
  • [4] H. Duru, Fonksiyonel Analiz, Nobel, Ankara, (2023).
  • [5] A.F. Filippov, Classical solutions of differential equations with multi-valued right-hand side, SIAM J. Control, 5 (1967), 609-621.
  • [6] H. Frankowska and T. Lorenz, Filippov’s theorem for mutational inclusions in a metric space, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 24(2) (2023), 1053-1094.
  • [7] A. Fryszkowski and J. Sadowski, Filippov lemma for measure differential inclusion, Math. Nachr. 294(3), (2021), 580-602.
  • [8] R. Gama and G. Smirnov, Stability and optimality of solutions to differential inclusions via averaging method, Set-Valued Var. Anal. 22(2), (2014), 349-374.
  • [9] C. Glocker, Set-Valued Force Laws: Dynamics of Non-Smooth Systems, Springer-Verlag, Berlin, (2001).
  • [10] P. Gorka and P. Rybka, Existence and uniqueness of solutions to singular ODE’s, Arch. Math., 94 (2010), 227-233.
  • [11] A. Iqbal, N.N. Abd Hamid, A.I.M. Ismail and M. Abbas, Galerkin approximation with quintic B-spline as basis and weight functions for solving second order coupled nonlinear Schrodinger equations ¨ , Math. Comput. Simul., 187 (2021), 1–16.
  • [12] M.K. Iqbal, M. Abbas, T. Nazir and N. Ali, Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto-Sivashinsky equation, Adv. Diff. Eqs., 2020 (2020), 558.
  • [13] N. Khalid, M. Abbas and M.K. Iqbal, Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms, Appl. Math. Comput., 349 (2019), 393–407.
  • [14] N. Khalid, M. Abbas, M.K. Iqbal, J. Singh and A.I.M. Ismail, A computational approach for solving time fractional differential equation via spline functions, Alexandria Eng. J., 59(1) (2020), 3061–3078.
  • [15] V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Springer Dordrecht, (1999).
  • [16] A. Majeed, M. Kamran, M. Abbas and M.Y.B. Misro, An efficient numerical scheme for the simulation of time-fractional nonhomogeneous Benjamin-Bona-Mahony-Burger model, Phys. Scr., 96(8) (2021), 084002.
  • [17] M. D. P. M. Marques, Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Birkhauser, Basel, (1993).
  • [18] T. Nazir, M. Abbas, A.I.M. Ismail, A.A. Majid and A. Rashid, The numerical solution of advection–diffusion problems using new cubic trigonometric B-splines approach, Appl. Math. Model., 40 (2016), 4586–4611.
  • [19] T. Nazir, M. Abbas and M.K. Iqbal, New cubic B-spline approximation technique for numerical solutions of coupled viscous Burgers equations, Eng. Comput., 38(1) (2020), 83–106.
  • [20] D. Repovs and P. Semenov, ˇ Continuous Selections of Multivalued Mappings, Springer Dordrecht, (1998).
  • [21] G.V. Smirnov, Introduction to the Theory of Differential Inclusions, A.M.S., Providence, Rhode Islands, (2002).
  • [22] R.B. Vinter, Optimal Control, Birkhauser, Boston, (2000).
  • [23] M. Yaseen, M. Abbas, T. Nazir and D. Baleanu, A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation, Adv. Differ. Equ., 2017(1) (2017), 1-18.

Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space

Yıl 2023, Cilt: 6 Sayı: 4, 188 - 193, 31.12.2023

Serkan İlter

https://doi.org/10.33401/fujma.1333804

Öz

In this paper, we present an existence theorem for the problem of discontinuous dynamical system related to ordinary differential inclusion, based on the use of the concepts related to weighted spaces introduced by Gorka and Rybka, without using any fixed point theorem. The solution concept in this theorem is considered to belong to the weighted space. For comparison with the classical case and as an application of the theorem, we give an example problem that has such a solution but no continuously differentiable solution.

Anahtar Kelimeler

Differential inclusion Weighted space Existence

Kaynakça

  • [1] M. Abbas, A.A. Majid, A.I.M. Ismail and A. Rashid, The application of cubic trigonometric B-spline to the numerical solution of the hyperbolic problems, Appl. Math. Comput., 239 (2014), 74–88.
  • [2] J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, (1990).
  • [3] P. Bettiol and H. Frankowska, Regularity of solution maps of differential inclusions under state constraints, Set-Valued Var. Anal., 15(1) (2007), 21-45.
  • [4] H. Duru, Fonksiyonel Analiz, Nobel, Ankara, (2023).
  • [5] A.F. Filippov, Classical solutions of differential equations with multi-valued right-hand side, SIAM J. Control, 5 (1967), 609-621.
  • [6] H. Frankowska and T. Lorenz, Filippov’s theorem for mutational inclusions in a metric space, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 24(2) (2023), 1053-1094.
  • [7] A. Fryszkowski and J. Sadowski, Filippov lemma for measure differential inclusion, Math. Nachr. 294(3), (2021), 580-602.
  • [8] R. Gama and G. Smirnov, Stability and optimality of solutions to differential inclusions via averaging method, Set-Valued Var. Anal. 22(2), (2014), 349-374.
  • [9] C. Glocker, Set-Valued Force Laws: Dynamics of Non-Smooth Systems, Springer-Verlag, Berlin, (2001).
  • [10] P. Gorka and P. Rybka, Existence and uniqueness of solutions to singular ODE’s, Arch. Math., 94 (2010), 227-233.
  • [11] A. Iqbal, N.N. Abd Hamid, A.I.M. Ismail and M. Abbas, Galerkin approximation with quintic B-spline as basis and weight functions for solving second order coupled nonlinear Schrodinger equations ¨ , Math. Comput. Simul., 187 (2021), 1–16.
  • [12] M.K. Iqbal, M. Abbas, T. Nazir and N. Ali, Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto-Sivashinsky equation, Adv. Diff. Eqs., 2020 (2020), 558.
  • [13] N. Khalid, M. Abbas and M.K. Iqbal, Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms, Appl. Math. Comput., 349 (2019), 393–407.
  • [14] N. Khalid, M. Abbas, M.K. Iqbal, J. Singh and A.I.M. Ismail, A computational approach for solving time fractional differential equation via spline functions, Alexandria Eng. J., 59(1) (2020), 3061–3078.
  • [15] V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Springer Dordrecht, (1999).
  • [16] A. Majeed, M. Kamran, M. Abbas and M.Y.B. Misro, An efficient numerical scheme for the simulation of time-fractional nonhomogeneous Benjamin-Bona-Mahony-Burger model, Phys. Scr., 96(8) (2021), 084002.
  • [17] M. D. P. M. Marques, Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Birkhauser, Basel, (1993).
  • [18] T. Nazir, M. Abbas, A.I.M. Ismail, A.A. Majid and A. Rashid, The numerical solution of advection–diffusion problems using new cubic trigonometric B-splines approach, Appl. Math. Model., 40 (2016), 4586–4611.
  • [19] T. Nazir, M. Abbas and M.K. Iqbal, New cubic B-spline approximation technique for numerical solutions of coupled viscous Burgers equations, Eng. Comput., 38(1) (2020), 83–106.
  • [20] D. Repovs and P. Semenov, ˇ Continuous Selections of Multivalued Mappings, Springer Dordrecht, (1998).
  • [21] G.V. Smirnov, Introduction to the Theory of Differential Inclusions, A.M.S., Providence, Rhode Islands, (2002).
  • [22] R.B. Vinter, Optimal Control, Birkhauser, Boston, (2000).
  • [23] M. Yaseen, M. Abbas, T. Nazir and D. Baleanu, A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation, Adv. Differ. Equ., 2017(1) (2017), 1-18.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalarda Dinamik Sistemler
Bölüm Makaleler
Yazarlar

Serkan İlter 0000-0002-7847-5124

Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 28 Temmuz 2023
Kabul Tarihi 30 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 4

Kaynak Göster

APA İlter, S. (2023). Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space. Fundamental Journal of Mathematics and Applications, 6(4), 188-193. https://doi.org/10.33401/fujma.1333804
AMA İlter S. Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space. FUJMA. Aralık 2023;6(4):188-193. doi:10.33401/fujma.1333804
Chicago İlter, Serkan. “Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space”. Fundamental Journal of Mathematics and Applications 6, sy. 4 (Aralık 2023): 188-93. https://doi.org/10.33401/fujma.1333804.
EndNote İlter S (01 Aralık 2023) Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space. Fundamental Journal of Mathematics and Applications 6 4 188–193.
IEEE S. İlter, “Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space”, FUJMA, c. 6, sy. 4, ss. 188–193, 2023, doi: 10.33401/fujma.1333804.
ISNAD İlter, Serkan. “Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space”. Fundamental Journal of Mathematics and Applications 6/4 (Aralık 2023), 188-193. https://doi.org/10.33401/fujma.1333804.
JAMA İlter S. Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space. FUJMA. 2023;6:188–193.
MLA İlter, Serkan. “Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space”. Fundamental Journal of Mathematics and Applications, c. 6, sy. 4, 2023, ss. 188-93, doi:10.33401/fujma.1333804.
Vancouver İlter S. Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space. FUJMA. 2023;6(4):188-93.
 Kapak Resmi İndir

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