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NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER

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

Mohammed M. Matar

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.

Anahtar Kelimeler

Fractional integro-di erential equations; Nonlocal condition; Exis- tence and Uniqueness; Fixed point 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

Mohammed M. Matar

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

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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