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NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER

Yıl 2016, Cilt: 4 Sayı: 1, 114 - 121, 01.04.2016

Öz

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.

Kaynakça

  • [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.
Yıl 2016, Cilt: 4 Sayı: 1, 114 - 121, 01.04.2016

Öz

Kaynakça

  • [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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Mohammed M. Matar Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2016
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

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. Nisan 2016;4(1):114-121.
Chicago Matar, Mohammed M. “NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER”. Konuralp Journal of Mathematics 4, sy. 1 (Nisan 2016): 114-21.
EndNote Matar MM (01 Nisan 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., c. 4, sy. 1, ss. 114–121, 2016.
ISNAD Matar, Mohammed M. “NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER”. Konuralp Journal of Mathematics 4/1 (Nisan 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, c. 4, sy. 1, 2016, ss. 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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