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

Yıl 2020, Cilt: 3 Sayı: 1, 166 - 175, 15.12.2020

Nihan Güngör

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• 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.