On nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces

• Autorzy: Kendre S. D. , Kharat V. V.

Identyfikatory

DOI

10.1515/jaa-2014-0018

• Języki publikacji: EN

Abstrakty

EN

In the present paper we investigate the existence and uniqueness of solutions of nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces. The technique used in our analysis is based on fixed point theorems and Pachpatte's integral inequality.

Słowa kluczowe

EN

mixed fractional integrodifferential equations; nonlocal condition; existence of solution

PL

mieszane ułamkowe równania różniczkowo-całkowe; warunki nielokalne; istnienie rozwiązania

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2014
• Tom: Vol. 20, nr 2
• Strony: 167--175
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kendre S. D.

• Department of Mathematics, University of Pune, Pune-41100, India

autor

Kharat V. V.

• Department of Mathematics, N. K. Orchid College of Engineering and Technology, Solapur-413002, India

Bibliografia

• [1] K. Balchandran and J. Y. Park, Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear. Anal. 71 (2009), 4471-4475.
• [2] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505.
• [3] L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Anal. Appl. 40 (1991), 11-19.
• [4] K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, j. Math. Anal. Appl. 179 (1993), 630-637.
• [5] M. B. Dhakne and S. D. Kendre, On abstract nonlinear mixed Volterra-Fredholm integro-differential equations, Comm. Appl. Nonlinear Anal. 13 (2006), no. 4, 101-112.
• [6] M. B. Dhakne and H. L. Tidke, Existence and uniqueness of solutions of nonlinear mixed integrodifferential equations with nonlocal condition in Banach spaces, Electron. J. Differential Equations 2011 (2011), Paper No. 31.
• [7] X. Dong, J. Wang and Y. Zhou, On nonlocal problems for fractional differential equations in Banach spaces, Opuscula Math. 31 (2011), 341-347.
• [8] S. D. Kendre, T. B. Jagtap and V. V. Kharat, On nonlinear fractional integrodifferential equations with non local condition in Banach spaces, Nonlinear Anal. Differential Equations 1 (2013), no. 3, 129-141.
• [9] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier, Amsterdam, 2006.
• [10] V. Lakshmikantham, S. Leela and J.V. Devi, Theory of fractional dynamic systems, Cambridge Scientific Publishers, Cambridge, 2009.
• [11] G. M. N’Guerekata, A Cauchy problem for some fractional differential abstract differential equation with nonlocal conditions, Nonlinear Anal. 70 (2009), 1873-1876.
• [12] B. G. Pachpatte, A note on certain integral inequality, Tamkang J. Math. 33 (2002), no. 4, 353-358.
• [13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
• [14] J. Wang, W. Wei and Y. Yang, On some impulsive fractional differential equations in Banach spaces, Opuscula Math. 30 (2010), 507-525.
• [15] Y. Yang and J. Wang, On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces, Opuscula Math. 31 (2011), 443-455.