Existence Solution for Nonlinear System of Fractional Integrodifferential Equations of Volterra Type with Fractional Boundary Conditions

Authors

  • Faraj Y. Ishak University of Duhok

DOI:

https://doi.org/10.15642/mantik.2020.6.1.1-12

Keywords:

Existence and uniqueness; stability; Fractional Integrodifferential equations; boundary value problem; existence and uniqueness theorem

Abstract

This article investigates existence, uniqueness and stability solutions of new fractional Volterra integro-differential equations system with fractional boundary conditions by using the existence and uniqueness theorem. Theorems on existence and uniqueness of solution are established under some necessary and sufficient conditions on compact space. A simple example of application of the main results of this article is presented.

Downloads

Download data is not yet available.

Author Biography

Faraj Y. Ishak, University of Duhok

 

 

References

Podlubny, I: Fractional differential equations, mathematics in science and engineering. Academic Press, New York/London/Toronto (1999)

R. Hilfer, Applications of Fractional Calculus in Physics. World Scientific,Singapore (2000).

V. Kac and P. Cheung, Quantum Calculus, Springer, New York, NY, USA, 2002.

V. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer-Verlag, New York (2011).

M. H. Annaby and Z. S. Mansour, q-Fractional Calculus and Equations, Springer, Berlin, Germany, 2012.

W. A. Al-Salam, “Some fractional q-integrals and q-derivatives,”Proceedings of the Edinburgh Mathematical Society, vol. 15, pp.135–140, 1966-1967.

R. P. Agarwal, “Certain fractional q-integrals and q-derivatives,”Proceedings of the Cambridge Philosophical Society, vol. 66, pp.365–370, 1969.

P. M. Rajkovi´c, S. D. Marinkovi´c, and M. S. Stankovi´c, “Fractional integrals and derivatives in q-calculus,” Applicable Analysis and Discrete Mathematics, vol. 1, no. 1, pp. 311–323, 2007.

M. H. Annaby and Z. S.Mansour, “q-Taylor and interpolation series for Jackson q-difference operators,” Journal of Mathematical Analysis and Applications, vol. 344, no. 1, pp. 472–483, 2008

J. Henderson and R. Luca, Positive solutions for a system of nonlocal fractional boundary value problems. Fract. Calc. Appl. Anal. 16, No 4 (2012), 985–1008; DOI: 10.2478/s13540-013-0061-4.

J. R. Graef, L. Kong, Q. Kong, and M. Wang, Uniqueness of positive solutions of fractional boundary value problems withnon-homogeneous integral boundary conditions. Fract. Calc. Appl. Anal. 15, No 3 (2012).

J. R. Graef, L. Kong, and B. Yang, Positive solutions for a semi posit one fractional boundary value problem with a forcing term. Fract. Calc.Appl. Anal. 15, No 1 (2012), 8–24; DOI: 10.2478/ s13540-012-0002-7; http://link.springer.com/article/10.2478/s13540-012-0002-7.

J. R. Graef, L. Kong, Q. Kong, and M. Wang, Fractional bound a ray value problem with integral boundary conditions. Appl. Anal. 92(2013).

J. R. Graef and L. Kong, Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives. Fract. Calc. Appl. Anal. 16, No 3 (2013), 695–708; DOI: 10.2478/s13540-013-0044-5; http://link.springer.com/article/10.2478/s13540-013-0044-5.

J. R. Graef, L. Kong, Q. Kong, and M. Wang, Positive solutions of nonlocal fractional boundary value problems. Discrete Contin. Dyn. Syst., Suppl. 2013.

J. R. Graef, L. Kong, Q. Kong, and M. Wang, Existence and uniqueness of solutions for a fractional boundary value problem with Dirichlet boundary condition. Electron. J. Qual. Theory Differ. Equ. 2013.

N. Nyamoradi and H. Alaei Dizaji “Existence solutions for nonlocal fractional differential equation with nonlinear boundary conditions”, IJST (2014) 38A4: 455-461 Iranian Journal of Science & Technology.

N. Nyamoradi and H. Alaei Dizaji, “Existence solutions for nonlocal fractional differential equation with nonlinear boundary conditions”, Iranian Journal of Science & Technology IJST (2014) 38A4: 455-461.

Zhenyu GUO, Min LIU, and Zhijing WANG, “Existence and Uniqueness of Solutions for a Nonlinear Fractional Integrodifferential Equation with Three-Point Fractional Boundary Conditions”, Journal of Mathematical Research with Applications, Vol. 36, No. 1, pp. 79–86, Jan 2016. DOI: 10.3770/j.issn:2095-2651.2016.01.010.

Butris and Ishak, “Some result’s in the theory of fractional integral equations of Volterra-Fredholm types “, Volume 9, No.1, January – February 2020 International Journal of Information Systems and Computer Sciences https://doi.org/10.30534/ijiscs/2020.

Downloads

Published

2020-05-30

How to Cite

Ishak, F. Y. (2020). Existence Solution for Nonlinear System of Fractional Integrodifferential Equations of Volterra Type with Fractional Boundary Conditions. Jurnal Matematika MANTIK, 6(1), 1–12. https://doi.org/10.15642/mantik.2020.6.1.1-12

Issue

Vol. 6 No. 1 (2020): Mathematics and Applied Mathematics

Section

Articles

License

Authors who publish with this journal agree to the following terms:
  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work