EXISTENCE AND UNIQUENESS RESULTS FOR CERTAIN FRACTIONAL BOUNDARY VALUE PROBLEMS
Keywords:
Existence theorem, Riemann-Liouville fractional derivative, Riemann-Liouville fractional integral.
Abstract
In this study, by applying some fixed point theorems when , the existence and uniqueness theorem for certain fractional differential equations with fractional boundary conditions is established. The theories are illustrated by examples.
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References
Afshari H., Marasi H., and Aydi H., Existence and Uniqueness of Positive Solutions for Boundary Value Problems of Fractional Differential Equations, Filomat, 31(9),(2017), 2675-2682.
Arora H.L. and J. G Al-Shamani, Stability of differential equation of non integer order through fixed point in the large, Indian J. pure ,appl. Math.,11(3)(1980),307-313.
Barrett J.H., Differential Equation of non-integer order, canad. J. Math.,6(4)(1954),529-541.
Benchora M., J. Henderson, S.K. Natouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008), pp. 1340-1350.
Dumitru Baleanu, Sayyedeh Zahra Nazemi, Shahram Rezapour, Existence and uniqueness of solutions for multi-term nonlinear fractional integro-differential equations, Advances in Difference Equations, Advances in Difference Equations 2013, 2013:368, 2-17.
[6] Kilbas A.A., H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V, Amsterdam (2006).
Krasnosel’skii M. A. , “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, no. 1(63), pp. 123–127,(1955).
Lakshmikanthama V., A.S.Vatsalab, Basic theory of fractional differential equations, -Nonlinear Analysis: Theory, Methods and Applications, Volume 69, Issue 8, 15 October 2008, pp. 2677-2682.
Liu Yuji. “Existence of Unbounded Positive Solutions of Boundary Value Problems for Differential Systems on Whole Lines.” Filomat, vol. 30, no. 13, 2016, pp. 3547–3564.
Oldham, K.B. and Spanier, J., The Fractional Calculus, Academic Press, New York, London(1974).
Podlubny I., Fractional differential equation, Mathematics in Science and Engineering. Academic Press, San Diego(1999).
Rabha W Ibrahim, A Kılıçman, FH Damag, Existence and uniqueness for a class of iterative fractional differential equations, Advances in Difference Equations 2015 (1), 78.
Rian Yan, Shurong Sun, Ying Sun, Zhenlai Han, Boundary value problems for fractional differential equations with nonlocal boundary conditions, Advances in Difference Equations, 2013, 2013:176,2-12.
Shaher M. Momani, “Local and global existence theorem on fractional integro-differential equations”, Journal of Fractional Calculus, Vol. 18, pp.81-86, (2000).
Shayma Adil Murad, Samir Hadid "An existence and uniqueness theorem for fractional differential equation with integral boundary condition", J. Frac. Calc. Appl 3 (6),2012, 1-9.
Shayma A. Murad, Hussein J.Zekri and Samir Hadid, “Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions”, International Journal of Differential Equations , Volume 2011, Article ID 304570, 15 pages.
Shuman Meng and Yujun Cui1, The Uniqueness Theorem of the Solution for a Class of Differential Systems with Coupled Integral Boundary Conditions", Discrete Dynamics in Nature and Society, Volume 2018, Article ID 9601868, 7 pages. https://doi.org/10.1155/2018/9601868.
Yongqing Wang, Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems , Journal of Function Spaces, Volume 2018, Article ID 1547293, 7 pages.
Arora H.L. and J. G Al-Shamani, Stability of differential equation of non integer order through fixed point in the large, Indian J. pure ,appl. Math.,11(3)(1980),307-313.
Barrett J.H., Differential Equation of non-integer order, canad. J. Math.,6(4)(1954),529-541.
Benchora M., J. Henderson, S.K. Natouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008), pp. 1340-1350.
Dumitru Baleanu, Sayyedeh Zahra Nazemi, Shahram Rezapour, Existence and uniqueness of solutions for multi-term nonlinear fractional integro-differential equations, Advances in Difference Equations, Advances in Difference Equations 2013, 2013:368, 2-17.
[6] Kilbas A.A., H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V, Amsterdam (2006).
Krasnosel’skii M. A. , “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, no. 1(63), pp. 123–127,(1955).
Lakshmikanthama V., A.S.Vatsalab, Basic theory of fractional differential equations, -Nonlinear Analysis: Theory, Methods and Applications, Volume 69, Issue 8, 15 October 2008, pp. 2677-2682.
Liu Yuji. “Existence of Unbounded Positive Solutions of Boundary Value Problems for Differential Systems on Whole Lines.” Filomat, vol. 30, no. 13, 2016, pp. 3547–3564.
Oldham, K.B. and Spanier, J., The Fractional Calculus, Academic Press, New York, London(1974).
Podlubny I., Fractional differential equation, Mathematics in Science and Engineering. Academic Press, San Diego(1999).
Rabha W Ibrahim, A Kılıçman, FH Damag, Existence and uniqueness for a class of iterative fractional differential equations, Advances in Difference Equations 2015 (1), 78.
Rian Yan, Shurong Sun, Ying Sun, Zhenlai Han, Boundary value problems for fractional differential equations with nonlocal boundary conditions, Advances in Difference Equations, 2013, 2013:176,2-12.
Shaher M. Momani, “Local and global existence theorem on fractional integro-differential equations”, Journal of Fractional Calculus, Vol. 18, pp.81-86, (2000).
Shayma Adil Murad, Samir Hadid "An existence and uniqueness theorem for fractional differential equation with integral boundary condition", J. Frac. Calc. Appl 3 (6),2012, 1-9.
Shayma A. Murad, Hussein J.Zekri and Samir Hadid, “Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions”, International Journal of Differential Equations , Volume 2011, Article ID 304570, 15 pages.
Shuman Meng and Yujun Cui1, The Uniqueness Theorem of the Solution for a Class of Differential Systems with Coupled Integral Boundary Conditions", Discrete Dynamics in Nature and Society, Volume 2018, Article ID 9601868, 7 pages. https://doi.org/10.1155/2018/9601868.
Yongqing Wang, Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems , Journal of Function Spaces, Volume 2018, Article ID 1547293, 7 pages.
Published
2020-06-02
How to Cite
UoD, J. of D. U., ABDULQADER, D. N., & MURAD, S. A. (2020). EXISTENCE AND UNIQUENESS RESULTS FOR CERTAIN FRACTIONAL BOUNDARY VALUE PROBLEMS. Journal of Duhok University, 22(2), 76-88. https://doi.org/10.26682/sjuod.2019.22.2.9
Section
Pure and Engineering Sciences
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