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EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

Year 2018, Volume: 1 Issue: 2, 166 - 179, 31.07.2018

Abstract

We study in this paper, the existence results for initial value problems for hybrid fractional integro-dierential equations. By using fixed point theorems for the sum of three operators are used for proving the main results.An example is also given to demonstrate the applications of our main results.

References

  • Lakshmikantham, V., Vatsala, A. S., Basic theory of fractional differential equations, Nonlinear Anal. 69(8), 2677-2682 (2008).
  • Podlubny, I., Fractional Differential Equations, Academic Press, San Diego (1999).
  • Sabatier, J. Agrawal, O. P. Machado, JAT (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007).
  • Tariboon, J., Ntouyas, S. K., Sudsutad, W Fractional integral problems for fractional differential equations via Caputo derivative. Adv. Deffer. Equ. 181 (2014).
  • Ahmad, B., Ntouyas, S. K., A four-point nonlocal, integral boundary value problem for fractional differential equations of arbitrary order. Electron. J. Qual. Theory Differ. Equ. 2011, 22 (2011).
  • Ahmad, B., Sivasundaram, S., Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions. Commun. Appl. Anal. 13, 121-228 (2009).
  • Ahmad, B., Sivasundaram, S., On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order. Appl. Math. Comput. 217, 480-487 (2010).
  • Ahmad, B., Ntouyas, S. K., Alsaedi, A., Existence theorems for nonlocal multi-valued Hadamard fractional integro-differential boundary value problems. J. Inequal. Appl. 2014, 454 (2014).
  • Chen, W., Zhao, Y: Solvability of boundary value problems of nonlinear fractional differential equations. Adv. Differ. Equ. 2015, 36 (2015).
  • Zhao, Y., Sun, S., Han, Z., Li, Q., The existence of multiple positive solutions for boundary value problems of nonlinear fractional di erential equations. Commun. Nonlinear Sci. Numer. Simul. 16, 2086-2097 (2011).
  • Zhao, Y, Sun, S, Han, Z, Li, Q: Theory of fractional hybrid differential equations. Comput. Math. Appl. 62, 1312-1324 (2011).
  • Sun, S., Zhao, Y., Han, Z., Li, Y., The existence of solutions for boundary value problem of fractional hybrid differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 4961-4967 (2012).
  • Ahmad, B., Ntouyas, S. K., An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions. Abstr. Appl. Anal. 2014, Article ID 705809 (2014).
  • Dhage, B. C., Ntouyas, S. K., Existence results for boundary value problems for fractional hybrid differential inclusions.Topol. Methods Nonlinear Anal. 44, 229-238 (2014).
  • Zhao, Y., Wang, Y., Existence of solutions to boundary value problem of a class of nonlinear fractional differential equations. Adv. Differ. Equ. 2014, 174 (2014).
  • Ahmad, B., Ntouyas, S. K., Alsaedi, A., Existence results for a system of coupled hybrid fractional differential equations.Sci. World J. 2014, Article ID 426438 (2014).
  • Dhage, B. C., Lakshmikantham, V., Basic results on hybrid differential equations, Nonlinear Anal. Hybrid 4 (2010) 414-424.
  • Dhage, B. C., Basic results in the theory of hybrid differential equations with mixed perturbations of second type. Funct. Differ. Equ. 19, 1-20 (2012).
  • Dhage, B. C., A fixed point theorem in Banach algebras with applications to functional integral equations. Kyungpook Math. J. 44, 145-155 (2004).
  • M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equations with fractional order, Surveys in Mathematics and its Appl. 3, 1-12 (2008).
  • Surang Sitho, Sotiris K Ntouyas and Jessada Tariboon: Existence results for hybrid fractional integro-differential equations ,Boundary Value Problems (2015).
  • Y. Zhao, S. Suna, Z. Han, Q. Li, Theory of fractional hybrid differential equations, Computers and Mathematics with Appl. 62, 1312-1324 (2011).
Year 2018, Volume: 1 Issue: 2, 166 - 179, 31.07.2018

Abstract

References

  • Lakshmikantham, V., Vatsala, A. S., Basic theory of fractional differential equations, Nonlinear Anal. 69(8), 2677-2682 (2008).
  • Podlubny, I., Fractional Differential Equations, Academic Press, San Diego (1999).
  • Sabatier, J. Agrawal, O. P. Machado, JAT (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007).
  • Tariboon, J., Ntouyas, S. K., Sudsutad, W Fractional integral problems for fractional differential equations via Caputo derivative. Adv. Deffer. Equ. 181 (2014).
  • Ahmad, B., Ntouyas, S. K., A four-point nonlocal, integral boundary value problem for fractional differential equations of arbitrary order. Electron. J. Qual. Theory Differ. Equ. 2011, 22 (2011).
  • Ahmad, B., Sivasundaram, S., Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions. Commun. Appl. Anal. 13, 121-228 (2009).
  • Ahmad, B., Sivasundaram, S., On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order. Appl. Math. Comput. 217, 480-487 (2010).
  • Ahmad, B., Ntouyas, S. K., Alsaedi, A., Existence theorems for nonlocal multi-valued Hadamard fractional integro-differential boundary value problems. J. Inequal. Appl. 2014, 454 (2014).
  • Chen, W., Zhao, Y: Solvability of boundary value problems of nonlinear fractional differential equations. Adv. Differ. Equ. 2015, 36 (2015).
  • Zhao, Y., Sun, S., Han, Z., Li, Q., The existence of multiple positive solutions for boundary value problems of nonlinear fractional di erential equations. Commun. Nonlinear Sci. Numer. Simul. 16, 2086-2097 (2011).
  • Zhao, Y, Sun, S, Han, Z, Li, Q: Theory of fractional hybrid differential equations. Comput. Math. Appl. 62, 1312-1324 (2011).
  • Sun, S., Zhao, Y., Han, Z., Li, Y., The existence of solutions for boundary value problem of fractional hybrid differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 4961-4967 (2012).
  • Ahmad, B., Ntouyas, S. K., An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions. Abstr. Appl. Anal. 2014, Article ID 705809 (2014).
  • Dhage, B. C., Ntouyas, S. K., Existence results for boundary value problems for fractional hybrid differential inclusions.Topol. Methods Nonlinear Anal. 44, 229-238 (2014).
  • Zhao, Y., Wang, Y., Existence of solutions to boundary value problem of a class of nonlinear fractional differential equations. Adv. Differ. Equ. 2014, 174 (2014).
  • Ahmad, B., Ntouyas, S. K., Alsaedi, A., Existence results for a system of coupled hybrid fractional differential equations.Sci. World J. 2014, Article ID 426438 (2014).
  • Dhage, B. C., Lakshmikantham, V., Basic results on hybrid differential equations, Nonlinear Anal. Hybrid 4 (2010) 414-424.
  • Dhage, B. C., Basic results in the theory of hybrid differential equations with mixed perturbations of second type. Funct. Differ. Equ. 19, 1-20 (2012).
  • Dhage, B. C., A fixed point theorem in Banach algebras with applications to functional integral equations. Kyungpook Math. J. 44, 145-155 (2004).
  • M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equations with fractional order, Surveys in Mathematics and its Appl. 3, 1-12 (2008).
  • Surang Sitho, Sotiris K Ntouyas and Jessada Tariboon: Existence results for hybrid fractional integro-differential equations ,Boundary Value Problems (2015).
  • Y. Zhao, S. Suna, Z. Han, Q. Li, Theory of fractional hybrid differential equations, Computers and Mathematics with Appl. 62, 1312-1324 (2011).
There are 22 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Said Melliani 0000-0002-5150-1185

Khalid Hilal This is me

Mohamed Hannabou This is me

Publication Date July 31, 2018
Submission Date May 15, 2018
Acceptance Date August 5, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

APA Melliani, S., Hilal, K., & Hannabou, M. (2018). EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS. Journal of Universal Mathematics, 1(2), 166-179.
AMA Melliani S, Hilal K, Hannabou M. EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS. JUM. July 2018;1(2):166-179.
Chicago Melliani, Said, Khalid Hilal, and Mohamed Hannabou. “EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS”. Journal of Universal Mathematics 1, no. 2 (July 2018): 166-79.
EndNote Melliani S, Hilal K, Hannabou M (July 1, 2018) EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS. Journal of Universal Mathematics 1 2 166–179.
IEEE S. Melliani, K. Hilal, and M. Hannabou, “EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS”, JUM, vol. 1, no. 2, pp. 166–179, 2018.
ISNAD Melliani, Said et al. “EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS”. Journal of Universal Mathematics 1/2 (July 2018), 166-179.
JAMA Melliani S, Hilal K, Hannabou M. EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS. JUM. 2018;1:166–179.
MLA Melliani, Said et al. “EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS”. Journal of Universal Mathematics, vol. 1, no. 2, 2018, pp. 166-79.
Vancouver Melliani S, Hilal K, Hannabou M. EXISTENCE RESULTS IN THE THEORY OF HYBRID FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS. JUM. 2018;1(2):166-79.