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Year 2020, Volume: 3 Issue: 1, 166 - 175, 15.12.2020

Nihan Güngör

Abstract

References

  • 1 H. Brunner, Volterra Integral Equations : An Introduction to Theory and Applications, Cambridge University Press, 2017.
  • 2 A.F. Çakmak, F. Ba¸sar, On Line and Double Integrals in the Non-Newtonian Sense, AIP Conference Proceedings, 1611 (2014), 415-423.
  • 3 A.F. Çakmak, F. Ba¸sar, Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers, Abstr. Appl. Anal., (2014), Article ID 236124, 12 pages.
  • 4 C. Duyar, M. Erdoğan, On non-Newtonian Real Number Series, IOSR Journal of Mathematics, 12(6) (2016), 34-48.
  • 5 C. Duyar, O. Oğur, A Note on Topology of Non-Newtonian Real Numbers, IOSR Journal Of Mathematics, 13(6) (2017), 11-14.
  • 6 M. Erdoğan, C. Duyar, Non-Newtonian Improper Integrals, Journal of Science and Arts, 1(42) (2018), 49-74.
  • 7 N. Güngör, Some Geometric Properties of the Non-Newtonian Sequence Spaces lp (N), Math. Slovaca, 70 (3) (2020), 689-696.
  • 8 M. Grosmann, R. Katz , Non-Newtonian Calculus, Lee Press, Pigeon Cove Massachussets, 1972.
  • 9 M. Grosmann, An Introduction to Non-Newtonian Calculus, International Journal of Mathematical Education in Science and Technology, 10(4) (1979), 525-528.
  • 10 U. Kadak, M. Özlük, Generalized Runge-Kutta Methods with Respect to Non-Newtonian Calculus, Abstr. Appl. Anal., (2014), Article ID 594685.
  • 11 M. Krasnov, K. Kiselev, G. Makarenko, Problems and Exercises in Integral Equation, Mır Publishers, Moscow, 1971.
  • 12 W.V. Lovitt, Linear Integral Equations, Dover Publications Inc., New York, 1950.
  • 13 D.A. Maturi, The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple, Advances in Pure Mathematics, 9 (2019), 832-843. 14 M. Rahman, Integral Equations and Their Applications, WIT press, Boston, 2007.
  • 15 B. Sa˘gır, F. Erdo˘gan, On the Function Sequences and Series in the Non-Newtonian Calculus, Journal of Science and Arts, 4(49) (2019), 915-936.
  • 16 F. Smithies, Integral Equations, Cambridge University Press, London, 1958.
  • 17 V. Volterra, B. Hostinsky, Opérations Infinitésimales linéares, Herman, Paris, 1938.
  • 18 A. M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Springer Verlag Berlin Heidelberg, 2011.

The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind

Year 2020, Volume: 3 Issue: 1, 166 - 175, 15.12.2020

Nihan Güngör

Abstract

In this study, the Fredholm integral equations are defined in the sense of non-Newtonian calculus by using the concept of *-integral. The main aim of the study to research the solution of the linear non-Newtonian Fredholm integral equations of the second kind by using the successive approximations method with respect to the non-Newtonian calculus. The necessary conditions for the *-continuity and uniqueness of the solution of these equations are investigated and finally given some numerical examples.

Keywords

Non-Newtonian calculus, Non-Newtonian Fredholm integral equations, Successive approximations method

References

  • 1 H. Brunner, Volterra Integral Equations : An Introduction to Theory and Applications, Cambridge University Press, 2017.
  • 2 A.F. Çakmak, F. Ba¸sar, On Line and Double Integrals in the Non-Newtonian Sense, AIP Conference Proceedings, 1611 (2014), 415-423.
  • 3 A.F. Çakmak, F. Ba¸sar, Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers, Abstr. Appl. Anal., (2014), Article ID 236124, 12 pages.
  • 4 C. Duyar, M. Erdoğan, On non-Newtonian Real Number Series, IOSR Journal of Mathematics, 12(6) (2016), 34-48.
  • 5 C. Duyar, O. Oğur, A Note on Topology of Non-Newtonian Real Numbers, IOSR Journal Of Mathematics, 13(6) (2017), 11-14.
  • 6 M. Erdoğan, C. Duyar, Non-Newtonian Improper Integrals, Journal of Science and Arts, 1(42) (2018), 49-74.
  • 7 N. Güngör, Some Geometric Properties of the Non-Newtonian Sequence Spaces lp (N), Math. Slovaca, 70 (3) (2020), 689-696.
  • 8 M. Grosmann, R. Katz , Non-Newtonian Calculus, Lee Press, Pigeon Cove Massachussets, 1972.
  • 9 M. Grosmann, An Introduction to Non-Newtonian Calculus, International Journal of Mathematical Education in Science and Technology, 10(4) (1979), 525-528.
  • 10 U. Kadak, M. Özlük, Generalized Runge-Kutta Methods with Respect to Non-Newtonian Calculus, Abstr. Appl. Anal., (2014), Article ID 594685.
  • 11 M. Krasnov, K. Kiselev, G. Makarenko, Problems and Exercises in Integral Equation, Mır Publishers, Moscow, 1971.
  • 12 W.V. Lovitt, Linear Integral Equations, Dover Publications Inc., New York, 1950.
  • 13 D.A. Maturi, The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple, Advances in Pure Mathematics, 9 (2019), 832-843. 14 M. Rahman, Integral Equations and Their Applications, WIT press, Boston, 2007.
  • 15 B. Sa˘gır, F. Erdo˘gan, On the Function Sequences and Series in the Non-Newtonian Calculus, Journal of Science and Arts, 4(49) (2019), 915-936.
  • 16 F. Smithies, Integral Equations, Cambridge University Press, London, 1958.
  • 17 V. Volterra, B. Hostinsky, Opérations Infinitésimales linéares, Herman, Paris, 1938.
  • 18 A. M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Springer Verlag Berlin Heidelberg, 2011.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Conference Paper
Authors

Nihan Güngör

Acceptance Date October 20, 2020
Publication Date December 15, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Güngör, N. (2020). The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind. Conference Proceedings of Science and Technology, 3(1), 166-175.
AMA Güngör N. The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind. Conference Proceedings of Science and Technology. December 2020;3(1):166-175.
Chicago Güngör, Nihan. “The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 166-75.
EndNote Güngör N (December 1, 2020) The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind. Conference Proceedings of Science and Technology 3 1 166–175.
IEEE N. Güngör, “The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 166–175, 2020.
ISNAD Güngör, Nihan. “The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind”. Conference Proceedings of Science and Technology 3/1 (December2020), 166-175.
JAMA Güngör N. The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind. Conference Proceedings of Science and Technology. 2020;3:166–175.
MLA Güngör, Nihan. “The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 166-75.
Vancouver Güngör N. The Succesive Approximations Method for Solving Non-Newtonian Fredholm Integral Equations of the Second Kind. Conference Proceedings of Science and Technology. 2020;3(1):166-75.