Tytuł artykułu
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Języki publikacji
Abstrakty
The objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.
Wydawca
Czasopismo
Rocznik
Tom
Strony
263--272
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Mathematics, C.K. Thakur Arts, Commerce and Science College, New Panvel 410 206, India
autor
- Department of Mathematics, University of Pune, Pune 411007, India
Bibliografia
- [1] V. Berinde, Existence and approximation of solutions of some first order iterative differential equations, Miskolc Math. Notes 11 (2010), 13-26.
- [2] E. Eder, The functional differential equation x (t) = x(x(t)), J. Differential Equations 54 (1984), 390-400.
- [3] R. W. Ibrahim, Existence of iterative Cauchy fractional differential equations, Int. J. Math. Sci. 7 (2013), no. 3, 379-384.
- [4] R. W. Ibrahim, A. Kilicman and F. H. Damag, Existence and uniqueness for a class of iterative fractional differential equations, Adv. Differ. Equ. 421 (2015), Article No. 78.
- [5] S. D. Kendre, T. B. Jagtap and V. V. Kharat, On nonlinear fractional integrodifferential equations with nonlocal condition in Banach spaces, J. Nonlinear Anal. Differ. Equ. 1 (2013), no. 3, 129-141.
- [6] S. D. Kendre and V. V. Kharat, On nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces, J. Appl. Anal. 20 (2014), no. 2, 167-175.
- [7] S. D. Kendre, V. V. Kharat and Ramdas Narute, On existence of solution for iterative integrodifferential equations, J. Nonlinear Anal. Differ. Equ. 3 (2015), 123-131.
- [8] S. D. Kendre, V. V. Kharat and Ramdas Narute, On existence of solution for iterative integrodifferential equations with deviating arguments, Int. J. Comput. Appl. Math. 10 (2015), no. 2, 95-107.
- [9] S. D. Kendre, V. V. Kharat and Ramdas Narute, On existence of solution for mixed iterative integrodifferential equations, Adv. Differ. Equ. Control Process. 15 (2015), 53-66.
- [10] V. V. Kharat and T. B. Jagtap, Existence of iterative fractional differential equation with non local condition, J. Ind. Math. Soc. 83 (2016), no. 1-2, 97-106.
- [11] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
- [12] H. Liu and W. Li, The exact analytic solutions of a nonlinear differential iterative equation, Nonlinear Anal. 69 (2008), 2466-2478.
- [13] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
- [14] B. G. Pachpatte, A note on certain integral inequality, Tamkang J. Math. 33 (2002), no. 4, 353-358.
- [15] A. Pelczar, On some iterative-differential equations. II, Zeszyty Naukowe UJ Prace Mat. 13 (1969), 49-51.
- [16] M. Podisuk, On simple iterative ordinary differential equations, Science Asia 28 (2002), no. 2, 191-198.
- [17] M. Podisuk, More on simple iterative ordinary differential equation, Proc. Soc. Behavioral Sci. 88 (2013), 187-195.
- [18] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
- [19] X.-P. Wang and J.-G. Si, Analytic solutions of an iterative functional differential equation, J. Math. Anal. Appl. 262 (2001), 490-498.
- [20] S. I. Unhale and S. D. Kendre, Existence and uniqueness results for iterative Volterra integrodifferential equation of fractional order, Comm. Appl. Nonlinear Anal. 25 (2018), 81-91.
- [21] D. Yang and W. Zhang, Solution of equivariance for iterative differential equations, Appl. Math. Lett. 17 (2004), 759-765.
- [22] P. Zhang and X. Gong, Existence of solutions for iterative differential equations, Electron. J. Differential Equations 2014 (2014), no. 7, 1-10.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
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