Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Influence of Coupled Nonlocal Slit-Strip Conditions Involving Caputo Derivative in Fractional Boundary Value Problem

Discontinuity, Nonlinearity, and Complexity 8(4) (2019) 429--445 | DOI:10.5890/DNC.2019.12.007

M. Subramanian, A.R. Vidhya Kumar, T. Nandha Gopal

Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamilnadu, India

Download Full Text PDF



By employing the coupled nonlocal slit-strips integral boundary conditions involving Caputo derivative, we investigate the existence and uniqueness of a boundary value problem of fractional differential equations. The main result is illustrated with examples.


  1. [1]  Podlubny, I. (1999), Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications, Academic Press, San Diego-Boston- New York-London-Tokyo-Toronto.
  2. [2]  Sabatier, J., Agrawal, O.P., and Tenreiro Machado, J.A. (2007), Advances in fractional calculus: theoretical developments and applications in physics and engineering, Springer Netherlands.
  3. [3]  Miller, K.S. and Ross, B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, Newyork.
  4. [4]  Diethelm, K. (2010), The Analysis of Fractional Differential Equations, Springer, Berlin, Heidelberg.
  5. [5]  Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006), Theory and applications of fractional differential equations, Amsterdam, Boston, Elsevier.
  6. [6]  Klafter, J., Lim, S.C., and Metzler, R. (2012), Fractional dynamics: Recent advances,World Scientific.
  7. [7]  ur Rehman, M. and Khan, R.A. (2010), Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations, Applied Mathematics Letters, 23, 1038-1044.
  8. [8]  Ahmad, B. and Nieto, J.J. (2011), Anti-periodic fractional boundary value problems, Computers and Mathematics with Applications, 62, 1150-1156.
  9. [9]  Zhou,W.X. and Chu, Y.D. (2012), Existence of solutions for fractional differential equations with multi-point boundary conditions, Communication Nonlinear Science Numerical and Simulation, 17, 1142-1148.
  10. [10]  Agarwal, Ravi.P., Ahmad, B., Garout, Doa’s., and Alsaedi, A. (2017), Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions, Chaos, Solitons and Fractals, DOI: 10.1016/j.chaos.2017.03.025.
  11. [11]  Ahmad, B., Alsaedi, A., and Alsharif, Alaa. (2015), Existence results for fractional-order differential equations with nonlocal multi-point-strip conditions involving Caputo derivative, Advances in Difference Equations, DOI:10.1186/s13622-015-0684-3.
  12. [12]  Ahmad, B. and Ntouyas, S.K. (2012), Existence of solutions for fractional differential inclusions with nonlocal strip conditions, Arab Journal of Mathematical Sciences, 18, 121-134.
  13. [13]  Ahmad, B. and Ntouyas, S.K. (2012), Existence results for nonlocal boundary value problems of fractional differential equations and inclusions with strip conditions, Boundary Value Problems, DOI: 10.1186/1687-2770-2012-55.
  14. [14]  Ahmad, B., Alsaedi, A., and Garout, Doa’s. (2016), Existence results for Liouville-Caputo type fractional differential equations with nonlocal multi-point and sub-strips boundary conditions, Computers and Mathematics with Applications, DOI: 10.1016/j.camwa.2016.04.015.
  15. [15]  Ahmad, B., Ntouyas, S.K., Agarwal, Ravi.P., and Alsaedi, A. (2015), Existence results for sequential fractional integrodifferential equations with nonlocal multi-point and strip conditions, Fractional Calculus & Applied Analysis, 18, 261-280.
  16. [16]  Ahmad, B. and Ntouyas, S.K. (2017), A coupled system of nonlocal fractional differential equations with coupled and uncoupled slit-strips type integral boundary conditions, Journal of Mathematical Sciences, 226(3), DOI: 10.1007/s10958-017-3528-8.