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NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER

Year 2016, Volume: 4 Issue: 1, 114 - 121, 01.04.2016

Abstract

In this paper, we investigate the existence and uniqueness of some nonlocal boundary condition for fractional integro-di erential equations with any order. The results are obtained by using xed point theorems. An example is introduced to illustrate the theorem.

References

  • [1] Agrawal, R. P., Benchohra, M., Hamani, S., Boundary value problems for fractional di eren- tial equations, Georgian Mathematical Journal, 16(3)(2009), 401-411.
  • [2] Agarwal, R. P., Ahmad B., Existence theory for anti-periodic boundary value problems of fractional di erential equations and inclusions, Computers & Mathematics with Applica- tions, 62(2011), 1200-1214.
  • [3] Balachandran, K., Park, J. Y., Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Analysis, 71(2009), 4471-4475.
  • [4] Benchohra, M., Hamani, S., and Ntouyas S. K., Boundary value problems for di erential equations with fractional order and nonlocal conditions, Nonlinear Analysis, 71(2009), 2391- 2396.
  • [5] N'guerekata, G. M., A Cauchy problem for some fractional abstract di erential equation with nonlocal condition, Nonlinear Analysis, 70(2009), 1873-1876.
  • [6] Delbosco, D., Rodino, L., Existence and uniqueness for a fractional di erential equation, Journal of Mathematical Analysis and Applications, 204(1996), 609-625.
  • [7] Matar M. M., Trujillo, J. J.,Existence of local solutions for di erential equations with arbi- trary fractional order, Arabian Journal of Mathematics, DOI 10.1007/s40065-015-0139-4
  • [8] Jaradat, O. K., Al-Omari, A., and Momani, S., Existence of the mild solution for fractional semilinear initial value problem, Nonlinear Analysis, 69(2008), 3153-3159.
  • [9] Lakshmikantham, V., Theory of fractional functional di erential equations, Nonlinear Anal- ysis, 69(2008), 3337-3343.
  • [10] Matar, M., On existence and uniqueness of the mild solution for fractional semilinear integro- di erential equations, Journal of Integral Equations and Applications, 23(3)(2011), 1-10.
  • [11] Matar, M., Existence and uniqueness of solutions to fractional semilinear mixed Volerra- Fredholm integrodi erential equations with nonlocal conditions, Electronic Journal of Di er- ential Equations, 155(2009), 1-7.
  • [12] Matar, M., Boundary value problem for fractional integro-di erential equations with nonlocal conditions, International Journal of Open Problems in Computer Science and Mathematics, 3(4)(2009), 481-489.
  • [13] Matar, M., El-Bohisie, F. A., On Existence of Solution for Higher-order Fractional Di eren- tial Inclusions with Anti-periodic Type Boundary conditions, British Journal of Mathematics & Computer Science, 7(5)(2015), 328-340.
  • [14] Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J., Theory and applications of fractional di erential equations, Elsevier, Amsterdam, 2006.
  • [15] Podlubny, I., Fractional di erential equations, Academic Press, New York, 1999.
  • [16] Zaslavsky, G. M., Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2005.
  • [17] Magin, R. L., Fractional Calculus in Bioengineering, Begell House Publisher, Connecticut, Conn, USA, 2006.
Year 2016, Volume: 4 Issue: 1, 114 - 121, 01.04.2016

Abstract

References

  • [1] Agrawal, R. P., Benchohra, M., Hamani, S., Boundary value problems for fractional di eren- tial equations, Georgian Mathematical Journal, 16(3)(2009), 401-411.
  • [2] Agarwal, R. P., Ahmad B., Existence theory for anti-periodic boundary value problems of fractional di erential equations and inclusions, Computers & Mathematics with Applica- tions, 62(2011), 1200-1214.
  • [3] Balachandran, K., Park, J. Y., Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Analysis, 71(2009), 4471-4475.
  • [4] Benchohra, M., Hamani, S., and Ntouyas S. K., Boundary value problems for di erential equations with fractional order and nonlocal conditions, Nonlinear Analysis, 71(2009), 2391- 2396.
  • [5] N'guerekata, G. M., A Cauchy problem for some fractional abstract di erential equation with nonlocal condition, Nonlinear Analysis, 70(2009), 1873-1876.
  • [6] Delbosco, D., Rodino, L., Existence and uniqueness for a fractional di erential equation, Journal of Mathematical Analysis and Applications, 204(1996), 609-625.
  • [7] Matar M. M., Trujillo, J. J.,Existence of local solutions for di erential equations with arbi- trary fractional order, Arabian Journal of Mathematics, DOI 10.1007/s40065-015-0139-4
  • [8] Jaradat, O. K., Al-Omari, A., and Momani, S., Existence of the mild solution for fractional semilinear initial value problem, Nonlinear Analysis, 69(2008), 3153-3159.
  • [9] Lakshmikantham, V., Theory of fractional functional di erential equations, Nonlinear Anal- ysis, 69(2008), 3337-3343.
  • [10] Matar, M., On existence and uniqueness of the mild solution for fractional semilinear integro- di erential equations, Journal of Integral Equations and Applications, 23(3)(2011), 1-10.
  • [11] Matar, M., Existence and uniqueness of solutions to fractional semilinear mixed Volerra- Fredholm integrodi erential equations with nonlocal conditions, Electronic Journal of Di er- ential Equations, 155(2009), 1-7.
  • [12] Matar, M., Boundary value problem for fractional integro-di erential equations with nonlocal conditions, International Journal of Open Problems in Computer Science and Mathematics, 3(4)(2009), 481-489.
  • [13] Matar, M., El-Bohisie, F. A., On Existence of Solution for Higher-order Fractional Di eren- tial Inclusions with Anti-periodic Type Boundary conditions, British Journal of Mathematics & Computer Science, 7(5)(2015), 328-340.
  • [14] Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J., Theory and applications of fractional di erential equations, Elsevier, Amsterdam, 2006.
  • [15] Podlubny, I., Fractional di erential equations, Academic Press, New York, 1999.
  • [16] Zaslavsky, G. M., Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2005.
  • [17] Magin, R. L., Fractional Calculus in Bioengineering, Begell House Publisher, Connecticut, Conn, USA, 2006.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mohammed M. Matar This is me

Publication Date April 1, 2016
Submission Date July 10, 2014
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Matar, M. M. (2016). NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER. Konuralp Journal of Mathematics, 4(1), 114-121.
AMA Matar MM. NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER. Konuralp J. Math. April 2016;4(1):114-121.
Chicago Matar, Mohammed M. “NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 114-21.
EndNote Matar MM (April 1, 2016) NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER. Konuralp Journal of Mathematics 4 1 114–121.
IEEE M. M. Matar, “NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER”, Konuralp J. Math., vol. 4, no. 1, pp. 114–121, 2016.
ISNAD Matar, Mohammed M. “NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER”. Konuralp Journal of Mathematics 4/1 (April 2016), 114-121.
JAMA Matar MM. NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER. Konuralp J. Math. 2016;4:114–121.
MLA Matar, Mohammed M. “NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER”. Konuralp Journal of Mathematics, vol. 4, no. 1, 2016, pp. 114-21.
Vancouver Matar MM. NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER. Konuralp J. Math. 2016;4(1):114-21.
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