On Hadamard fractional integro-differential boundary value problems

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• 作者：Bashir Ahmad (1)
  Sotiris K. Ntouyas (2)
  
  1. Department of Mathematics ; Faculty of Science ; King Abdulaziz University ; P.O. Box 80203 ; Jeddah聽 ; 21589 ; Saudi Arabia
  2. Department of Mathematics ; University of Ioannina ; 451 10聽 ; Ioannina ; Greece
  
• 关键词：Hadamard fractional derivative ; Integral boundary conditions ; Fixed point theorems ; 34A60 ; 34A08
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：47
• 期：1-2
• 页码：119-131
• 全文大小：162 KB
• 参考文献：1. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
  2. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V, Amsterdam (2006)
  3. Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston (2012)
  4. Agarwal, R.P., Zhou, Y., He, Y.: Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59, 1095鈥?100 (2010) CrossRef
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  6. Ahmad, B., Nieto, J.J.: Riemann鈥揕iouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound. Value Probl. 36, 9 (2011)
  7. Ahmad, B., Ntouyas, S.K., Alsaedi, A.: New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ. 2011, 11 (2011). Article ID 107384 CrossRef
  8. O鈥橰egan, D., Stanek, S.: Fractional boundary value problems with singularities in space variables. Nonlinear Dyn. 71, 641鈥?52 (2013) CrossRef
  9. Ahmad, B., Ntouyas, S.K., Alsaedi, A.: A study of nonlinear fractional differential equations of arbitrary order with Riemann鈥揕iouville type multistrip boundary conditions. Math. Probl. Eng. 2013, 9 (2013). Article ID 320415
  10. Ahmad, B., Nieto, J.J.: Boundary value problems for a class of sequential integrodifferential equations of fractional order. J. Funct. Spaces Appl. 2013, 8 (2013). Article ID 149659 CrossRef
  11. Zhang, L., Ahmad, B., Wang, G., Agarwal, R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51鈥?6 (2013) CrossRef
  12. Liu, X., Jia, M., Ge, W.: Multiple solutions of a p-Laplacian model involving a fractional derivative. Adv. Differ. Equ. 2013, 126 (2013) CrossRef
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  15. Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Compositions of Hadamard-type fractional integration operators and the semigroup property. J. Math. Anal. Appl. 269, 387鈥?00 (2002) CrossRef
  16. Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Fractional calculus in the Mellin setting and Hadamard-type fractional integrals. J. Math. Anal. Appl. 269, 1鈥?7 (2002) CrossRef
  17. Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Mellin transform analysis and integration by parts for Hadamard-type fractional integrals. J. Math. Anal. Appl. 270, 1鈥?5 (2002) CrossRef
  18. Kilbas, A.A.: Hadamard-type fractional calculus. J. Korean Math. Soc. 38, 1191鈥?204 (2001)
  19. Kilbas, A.A., Trujillo, J.J.: Hadamard-type integrals as G-transforms. Integr. Transform. Spec. Funct. 14, 413鈥?27 (2003) CrossRef
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  21. Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003) CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

In this paper, we study the existence and uniqueness of solutions for a fractional integral boundary value problem involving Hadamard type fractional differential equations and integral boundary conditions. Our results are new in the present configuration and are based on some classical ideas of fixed point theory. The paper concludes with some illustrative examples.