Analysis of boundary value problem with multi-point conditions involving Caputo-Hadamard fractional derivative

• Muthaiah, Subramanian ^[1] ; Gopal, Thangaraj Nandha ^[2]
  1. [1] KPR Institute of Engineering and Technology.
  2. [2] Sri Ramakrishna Mission Vidyalaya College of Arts and Science.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 6, 2020, págs. 1555-1575
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-06-0093
• Enlaces
  • Texto completo
• Resumen

  • We study the boundary value problems (BVPs) of the Caputo-Hadamard type fractional differential equations (FDEs) supplemented by multi-point conditions. Many new results of existence and uniqueness are obtained with the use of fixed point theorems for single-valued maps. With the help of examples, the results are well illustrated.

• Referencias bibliográficas
  • B. Ahmad and SK. Ntouyas, “Initial value problems for functional and neutral functional Hadamard type fractional differential inclusions”,...
  • B. Ahmad, SK. Ntouyas, R. P. Agarwal, and A. Alsaedi, “New results for boundary value problems of Hadamard-type fractional differential inclusions...
  • A. Ali, K. Shah, F. Jarad, V. Gupta, and T. Abdeljawad, “Existence and stability analysis to a coupled system of implicit type impulsive boundary...
  • Z. Ali, A. Zada, and K. Shah, “Existence and stability analysis of three point boundary value problem”, International journal of applied and...
  • D. W. Boyd and J. S. W. Wong, “On nonlinear contractions”, Proceedings of the American Mathematical Society, vol. 20, no. 2, pp. 458-464,...
  • P. Duraisamy, A. R. Vidhya Kumar, T. Nandha Gopal, and M. Subramanian, “Influence of nonlocal discrete and integral boundary conditions involving...
  • Y. Y. Gambo, F. Jarad, D. Baleanu, and T. Abdeljawad, “ On Caputo modification of the Hadamard fractional derivatives”, Advances in difference...
  • A. Guezane-Lakoud, G. Rebiai, and R. Khaldi, “Existence of solutions for a nonlinear fractional system with nonlocal boundary conditions”,...
  • A. Granas and J. Dugundji, Fixed point theory, New York, NY : Springer, 2003, doi: 10.1007/978-0-387-21593-8
  • J. Hadamard, “Essai sur letude des fonctions donnees par leur development de Taylor”, Journal de mathématiques pures et appliquées 4e série,...
  • A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations”, Amsterdam: Elsevier, 2006.
  • M. A. Krasnoselskii, “Two remarks on the method of successive approximations”, Uspekhi matematicheskikh nauk, vol. 10, no. 1, pp. 123-127,...
  • S. Muthaiah, M. Murugesan, and N. Thangaraj, “Existence of solutions for nonlocal boundary value problem of Hadamard fractional differential...
  • I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, some methods...
  • M. Qinghua, M. Chao, and J. Wang, “A Lyapunov-type inequality for a fractional differential equation with Hadamard derivative”, Journal of...
  • J. Sabatier, O. P. Agrawal, and J. A. Tenreiro Machado, Advances in fractional calculus: theoretical developments and applications in physics...
  • K. Shah, A. Ali, and S. Bushnaq, “Hyers-Ulam stability analysis to implicit Cauchy problem of fractional differential equations with impulsive...
  • M. Subramanian, A. R. Vidhya Kumar, and T. Nandha Gopal, “Analysis of fractional boundary value problem with non local flux multipoint conditions...
  • M. Subramanian, A. R. Vidhya Kumar, and T. Nandha Gopal, “A fundamental approach on non-integer order differential equation using nonlocal...
  • M. Subramanian, A. R. Vidhya Kumar, and T. Nandha Gopal, “Analysis of fractional boundary value problem with non-local integral strip boundary...
  • M. Subramanian, A. R. Vidhya Kumar, and T. Nandha Gopal, “Influence of coupled nonlocal slit-strip conditions involving Caputo derivative...
  • M. Subramanian, A. R. Vidhya Kumar, and T. Nandha Gopal, “A writ large analysis of complex order coupled differential equations in the ourse...
  • M. Subramanian, A. R. Vidhya Kumar, and T. Nandha Gopal, “A strategic view on the consequences of classical integral sub-strips and coupled...
  • P. Thiramanus, S. K. Ntouyas, and J. Tariboon, “Positive solutions for Hadamard fractional differential equations on infinite domain”, Advances...
  • E. Ugurlu, D. Baleanu, and K. Tas, “ On the solutions of a fractional boundary value problem”, Turkish journal of mathematics, vol. 42, no....
  • A. R. Vidhya Kumar, P. Duraisamy, T. Nandha Gopal and M. Subramanian, “Analysis of fractional differential equation involving Caputo derivative...
  • G. Wang, K. Pei, R. P. Agrawal, L. Zhang, and B. Ahmad, “Nonlocal Hadamard fractional boundary value problem with Hadamard integral and discrete...
  • T. A. Yildiz, N. Khodabakhshi and D. Baleanu, “Analysis of mixedorder Caputo fractional system with nonlocal integral boundary condition”,...
  • N. Yukunthorn, B. Ahmad, SK. Ntouyas, and J. Tariboon, “On Caputo-Hadamard type fractional impulsive hybrid systems with nonlinear fractional...
  • A. Zada, R. Rizwan, J. Xu, and Z. Fu, “On implicit impulsive Langevin equation involving mixed order derivatives”, Advances in difference...