Fractional Differential Equations with Anti-Periodic Boundary Conditions

REFERENCES

• R. P. Agarwal , M. Benchohra , and S. Hamani ( 2008 ). Boundary value problems for differential inclusions with fractional order . Adv. Stud. Contemp. Math. 12 ( 2 ): 181 – 196 .
   Google Scholar
• R. P. Agarwal , M. Benchohra , and S. Hamani ( 2009 ). Boundary value problems for fractional differential equations . Georgian Math. J. 12 : 401 – 411 .
   Google Scholar
• B. Ahmad and J. J. Nieto ( 2009 ). Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions . Bound. Value Probl. Art. 708576, pp. 11.
   Google Scholar
• B. Ahmad and J. J. Nieto ( 2008 ). Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions . Nonlinear. Anal. TMA 69 : 3291 – 3298 .
   Google Scholar
• B. Ahmad and J. J. Nieto ( 2010 ). Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray- Schauder degree theory . Topological Meth. Nonlinear Anal. 35 : 295 – 304 .
   Web of Science ®Google Scholar
• B. Ahmad and V. Otero-Espinar ( 2009 ). Existence of solutions for fractional differential inclusions with anti-periodic boundary conditions. Bound. Value Probl. Art. 625347, pp. 11.
   Google Scholar
• C. Ahn and C. Rim ( 1999 ). Boundary flows in general coset theories . J. Phys. A 32 : 2509 – 2525 .
   Google Scholar
• A. Abdurrahman , F. Anton , and J. Bordes ( 1993 ). Half-string oscillator approach to string field theory (ghost sector. I) . Nuclear Physics B 397 : 260 – 282 .
   Web of Science ®Google Scholar
• E. A. Barkova and P. P. Zabreko ( 2004 ). An analogue of Peano's theorem for fractional order quasilinear equations in compactly embedded scales of Banach spaces. (Russian) Differ. Uravn. 40:522–526, 575. [translation in Differ. Equ. 40:565–570]. .
   Google Scholar
• A. Belarbi , M. Benchohra , and A. Ouahab ( 2006 ). Existence results for functional differential equations of fractional order . Appl. Anal. 85 : 1459 – 1470 .
   Google Scholar
• M. Benchohra , J. R. Graef , and S. Hamani ( 2008 ). Existence results for boundary value problems with nonlinear fractional differential equations . Appl. Anal. 87 : 851 – 863 .
   Web of Science ®Google Scholar
• M. Benchohra , S. Hamani , and S. K. Ntouyas (2008). Boundary value problems for differential equations with fractional order. Surv. Math. Appl. 3:1–12.
   Google Scholar
• M. Benchohra , J. Henderson , S. K. Ntouyas , and A. Ouahab ( 2008 ). Existence results for fractional order functional differential equations with infinite delay . J. Math. Anal. Appl. 332 : 1340 – 1350 .
   Google Scholar
• Y. Chen , J. J. Nieto , and D. O'Regan ( 2007 ). Antiperiodic solutions for fully nonlinear first-order differential equations . Math. Comput. Model. 46 : 1183 – 1190 .
   Web of Science ®Google Scholar
• V. Daftardar-Gejji and S. Bhalekar ( 2008 ). Boundary value problems for multi-term fractional differential equations . J. Math. Anal. Appl. 345 : 754 – 765 .
   Web of Science ®Google Scholar
• D. Franco , J. J. Nieto , and D. O'Regan ( 2003 ). Anti-periodic boundary value problem for nonlinear first order ordinary differential equations . Math. Inequal. Appl. 6 : 477 – 485 .
   Web of Science ®Google Scholar
• R. Hilfer ( 2000 ). Applications of Fractional Calculus in Physics . World Scientific , Singapore .
   Google Scholar
• A. A. Kilbas , H. M. Srivastava , and J. J. Trujillo ( 2006 ). Theory and Applications of Fractional Differential Equations . North-Holland Mathematics Studies , Vol. 204 . Elsevier Science B.V. , Amsterdam .
   Google Scholar
• V. Lakshmikantham , S. Leela , and J. Vasundhara ( 2009 ). Theory of Fractional Dynamic Systems . Cambridge Academic Publishers , Cambridge , UK .
   Google Scholar
• Z. Luo , J. Shen , and J. J. Nieto ( 2005 ). Anti-periodic boundary value problem for first order impulsive ordinary differential equations . Comput. Math. Appl. 49 : 253 – 261 .
   Web of Science ®Google Scholar
• I. Podlubny ( 1999 ). Fractional Differential Equations . Academic Press , San Diego .
   Google Scholar
• X. Su and S. Zhang ( 2011 ). Unbounded solutions to a boundary value problem of fractional order on the half-line . Comput. Math. Appl. 61 : 1079 – 1087 .
   Web of Science ®Google Scholar
• K. Wang and Y. Li ( 2009 ). A note on existence of anti-periodic and heteroclinic solutions for a class of second-order odes . Nonlinear Anal. TMA 70 : 1711 – 1724 .
   Google Scholar
• W. Wang and J. Shen ( 2009 ). Existence of solutions for anti-periodic boundary value problems . Nonlinear Anal. TMA 70 : 598 – 605 .
   Google Scholar
• R. Wu , F. Cong , and Y. Li ( 2011 ). Anti-periodic solutions for second order differential equations . Appl. Math. Lett. 24 : 860 – 863 .
   Google Scholar