Existence and uniqueness results for a fractional differential equations with nonlocal boundary conditions
Resumo
In this paper, we establish sufficient conditions for the existence and uniqueness of solution of a boundary value problem of differential equations of fractional order involving the nonlocal boundary condition.
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Referências
R. W. Ibrahim, S. Momani, On the existence and uniqueness of solutions of a class of fractional differential equations, J. Math. Anal. Appl. 334 (1), 1-10, (2008). https://doi.org/10.1016/j.jmaa.2006.12.036
X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett. 22, 64-69, (2009). https://doi.org/10.1016/j.aml.2008.03.001
Y. Zhang, Z. Bai, T. Feng, Existence results for a coupled system of nonlinear fractional three-point boundary value problems at resonance, Comput. Math. Appl. 61, 1032-1047, (2011). https://doi.org/10.1016/j.camwa.2010.12.053
M. M. Matar, On existence of solution to nonlinear fractional differential equations for 0 ≤ α ≤ 3, J. Fract. Cal. Appl. 3(14), 1-8, (2012).
M. Houas, Z. Dahmani, New results for a coupled system of fractional differential equations, Facta A Universitatis (NIS) Ser. Math. Inform 28(2), 133-150, (2013).
J. Liang, Z. Liu, X. Wang, Solvability for a coupled system of nonlinear fractional differential equations in a Banach space, Fractional Calculus and Applied Analysis 16(1), 51-63, (2013). https://doi.org/10.2478/s13540-013-0004-0
S. K. Ntouyas, Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions, Differ. Incl. Control Optim. 33, 17-39, (2013). https://doi.org/10.7151/dmdico.1146
S. K. Ntouyas, Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions, Opusc. Math. 33, 117-138, (2013). https://doi.org/10.7494/OpMath.2013.33.1.117
M. H. Akrami, G. H. Erjaee, Existence uniqueness and well-posed conditions on a class of fractional differential equations with boundary condition, Journal of Fractional Calculus and Applications 6(2), 171-185, (2015).
S. Kumar, R. K. Vats, H. K. Nashine, Existence and uniqueness results for three-point nonlinear fractional (arbitrary order) boundary value problem, Matematicki Vesnik Journal 70(4), 314-325, (2018).
A. K. Nain, R. K. Vats, S. K. Verma, Existence and uniqueness results for positive solutions of Hadamard type fractional BVP, Journal of Interdisciplinary Mathematics 22(5), 697-710, (2019). https://doi.org/10.1080/09720502.2019.1661603
H. K. Nashine, R. W. Ibrahim, Monotone solutions of iterative fractional equations found by modified Darbo type fixed point theorems, Journal of Fixed Point Theory and Application 19, 3217-3229, (2017). https://doi.org/10.1007/s11784-017-0470-9
M. B. Zada, M. Sarwar, H. K. Nashine, Solution of infinite system of ordinary differential equations and fractional hybrid differential equations via measure of noncompactness, Journal of Taibah University for Science 13(1), 1119-1127, (2019). https://doi.org/10.1080/16583655.2019.1686862
M. Muslim, A. Kumar, M. Feˇckan, Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses, Journal of King Saud University-Science 30(2), 204-213, (2018). https://doi.org/10.1016/j.jksus.2016.11.005
D. Chalishajar, A. Kumar, Existence, uniqueness and Ulam's stability of solutions for a coupled system of fractional differential equations with integral boundary conditions, Mathematics 6(6), 96, (2018). https://doi.org/10.3390/math6060096
H. K. Nashine, R. W. Ibrahim, Symmetric solutions of nonlinear fractional integral equations via a new fixed point theorem under FG-contractive condition, Numerical Functional Analysis and Optimization 40(12), 1448-1466, (2019). https://doi.org/10.1080/01630563.2019.1602779
R. Arab, H. K. Nashine, N. H. Can, T. T. Binh, Solvability of functional-integral equations (fractional order) using measure of noncompactness, Advances in Difference Equations 12, 1-13, (2020). https://doi.org/10.1186/s13662-019-2487-4
I. J. Cabrera, B. Lopez, K. Sadarangani, Existence of positive solutions for the nonlinear elastic beam equation via a mixed monotone operator, Journal of Computational and Applied Mathematics 327, 306-313, (2018). https://doi.org/10.1016/j.cam.2017.04.031
L. Byszewski, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162, 494-505, (1991). https://doi.org/10.1016/0022-247X(91)90164-U
L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, Selected problems of mathematics, 50th Anniv. Cracow Univ. Technol. Anniv. 6, 25-33, (1995).
I. Podlubny, Fractional Differential Equations, Academic Press, New York, (1999).
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, (2006).
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Funding data
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Council of Scientific and Industrial Research, India
Grant numbers 25(0268)/17/EMR-II