Existence and stability results for nonlinear fractional integrodifferential equations with nonlocal antiperiodic boundary conditions
Resumo
This work examines the existence and stability of solutions for nonlinear fractional integrodifferential equations with nonlocal antiperiodic boundary conditions, which include the Caputo derivative. The existence established using Banach contraction mapping theorem. Furthermore, two types of Ulam stability are being studied, namely Ulam-Hyers stability and generalized Ulam-Hyers stability. Finally, examples are given to demonstrate the applicability of the key findings.
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Referências
B. Abdellatif, S.A. Mohamed and B. Maamar, Existence results for ψ-Caputo fractional neutral functional integrodifferential equations with finite delay, Turkish Journal of Mathematics, 44, (2020) 2380-2401.
R.P. Agarwal, M. Bohner and V.B. Shakhmurov, Linear and nonlinear nonlocal boundary value problems for differentialoperator equations, Applicable Analysis, 85(6-7), (2006) 701-716.
S.F. Aljurbua, Generalized existence results for solutions of nonlinear fractional differential equations with nonlocal boundary conditions, Ain Shams Engineering Journal, 15(11), (2024) 103035.
R. Almeida, A Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation, 44, (2017) 460-481.
N. Annapoorani and V. Umapathi, A study on fractional integrodifferential equations using tempered ψ-Caputo fractional derivative, Gulf Journal of Mathematics, 20(1), (2025) 289-302.
I. Ansari, R. Dubey, A. Devi and A. Kumar, Analyzing the existence and uniqueness of solutions in coupled fractional differential equations, International Journal of Applied and Computational Mathematics, 11(67), (2025).
A. Cabada and Z. Hamdi, Nonlinear fractional differential equations with integral boundary value conditions, Applied Mathematics and Computation, 228, (2014) 251-257.
A. Devi, A. Kumar, T. Abdeljawad and A. Khan, Existence and stability analysis of solutions for fractional Langevin equation with nonlocal integral and anti-periodic-type boundary conditions, Fractals, 28(8), (2020) 2040006.
F. Erkan, N.A. Hamal, S.K. Ntouyas and J. Tariboon, Existence and uniqueness analysis for (k, ψ)-Hilfer and (k, ψ)-Caputo sequential fractional differential equations and inclusions with non-separated boundary conditions, Fractal and Fractional, 9(7), (2025) 437.
J.F Gomez-Aguilar, R. Razo-Hernandez and D. Granados-Lieberman, A physical interpretation of fractional calculus in observables terms: Analysis of the fractional time constant and the transitory response, Revista Mexicana de Fisica, 60(1), (2014) 32-38.
J.R. Graef and J.R.L. Webb, Third order boundary value problems with nonlocal boundary conditions, Nonlinear Analysis: Theory, Methods and Applications, 71(5-6), (2009) 1542-1551.
K. Hattaf, On the stability and numerical scheme of fractional differential equations with application to biology, Computation, 10(6), (2022) 97.
A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 2006.
A. Lachouri, M.E. Samei and A. Ardjouni, Existence and stability analysis for a class of fractional pantograph qdifference equations with nonlocal boundary conditions, Boundary Value Problems, 2, (2023).
V. Lakshmikantham, S. Leela and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, Cambridge, 2009.
Y. Li, Y. Chen and I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Computers and Mathematics with Applications, 59(5), (2010) 1810-1821.
R. Ma, A survey on nonlocal boundary value problems, Applied Mathematics E-Notes 7, (2007) 257-279.
J.Y. Park, K. Balachandran and N. Annapoorani, Existence results for impulsive neutral functional integrodifferential equations with infinite delay, Nonlinear Analysis: Theory, Methods and Applications, 71(7-8), (2009) 3152-3162.
I. Petras, Fractional-Order Nonlinear Systems, Nonlinear Physical Science, Springer Berlin, 2011.
K.K. Saha, N. Sukavanam and S. Pan, Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions, Alexandria Engineering Journal, 72, (2023) 147-155.
A. Shaikh, S. Waghule, D. Patil and K.S. Nisar, A study of the Atangana Baleanu fractional differential equation with an application in gas dynamic problem, Baghdad Science Journal, 22(7), (2025) 2386-2401.
A. Tudorache and R. Luca, A Hadamard fractional boundary value problem on an infinite interval at resonance, Fractal and Fractional, 9(6), (2025) 378.
W. Sudsutad, C. Thaiprayoon and S.K. Ntouyas, Existence and stability results for ψ-Hilfer fractional integrodifferential equation with mixed nonlocal boundary conditions, Mathematics, 6(4), (2021) 4119-4141.
G. Wang, B. Ahmad and L. Zhang, Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Analysis: Theory, Methods and Applications, 74(3), (2011) 792-804.
Y. Zhou, J. Wang and L. Zhang, Basic Theory of Fractional Differential Equations, World Scientific, New Jersey, London, Singapore, 2014.
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