Existence Results for Sequential Fractional Differential Equations with Advanced Arguments
DOI:
https://doi.org/10.14419/4tmqrk79Published
07-06-2026Keywords:
Advanced arguments; boundary value problem; contraction mapping; fixed point theorem; sequential fractional differential equationsAbstract
The existence and uniqueness results for the sequential fractional differential equations involving Caputo differential operator with advanced arguments and boundary conditions are investigated in this paper. The uniqueness of the solution is established using the classical contraction mapping principle and the existence results are derived via D.O’Regan’s fixed point theorem. An example is presented to illustrate our findings.
References
[1] D.B. Dhaigude, B.H. Rizqan, Existence and uniqueness of solutions for fractional differential equations with advanced arguments, Advances in Mathematical Models and Applications, 2 (3) (2017) 240–250.
[2] H. Fallahgoul, S. Focardi, F. Fabozzi, Fractional Calculus and Fractional Processes with Applications to Financial Economics: Theory and Application, Academic Press, 2016.
[3] A. Granas, J. Dugundji, Fixed Point Theory, Springer, New York, 2003, pp. 15–16.
[4] T. Jankowski, Fractional problems with advanced arguments, Applied Mathematics and Computation, 230 (2014) 371–382.
[5] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Vol. 204, Elsevier, Amsterdam, 2006.
[6] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
[7] N. Nyamoradi, A. Razani, Existence to fractional critical equation with Hardy–Littlewood–Sobolev nonlinearities, Acta Mathematica Scientia, 41 (4) (2021) 1321–1332.
[8] B.H. Rizqan, D. Dhaigude, Nonlinear boundary value problem of fractional differential equations with arguments under integral boundary condition, Tamkang Journal of Mathematics, 51 (2) (2020) 101–112.
[9] B. Ahmad, M. Alnahdi, S.K. Ntouyas, Existence results for a differential equation involving the right Caputo fractional derivative and mixed nonlinearities with nonlocal closed boundary conditions, Fractal and Fractional, 7 (2) (2023) 129.
[10] B. Ahmad, J.J. Nieto, Sequential fractional differential equations with three-point boundary conditions, Computers and Mathematics with Applications, 64 (10) (2012) 3046–3052.
[11] B. Ahmad, A. Broom, A. Alsaedi, S.K. Ntouyas, Nonlinear integro-differential equations involving mixed right and left fractional derivatives and integrals with nonlocal boundary data, Mathematics, 8 (3) (2020) 336.
[12] A. Alsaedi, A. Broom, S.K. Ntouyas, B. Ahmad, Nonlocal fractional boundary value problems involving mixed right and left fractional derivatives and integrals, Axioms, 9 (2) (2020) 50.
[13] Z.A. Mohammed, M. Damak, F.S. Fadhel, H.S. Altahainah, Existence and uniqueness theorem of multi-dimensional integro-differential equations with fractional differointegrations, Babylonian Journal of Mathematics, 2025 (2025) 44–49.
[14] H. Benmehidi, M.Z. Sarikaya, Z. Dahmani, Existence results for a hybrid system of mixed differential equations with sequential fractional derivatives, Facta Universitatis, Series: Mathematics and Informatics, (2025) 319–332.
[15] A. Bragdi, A. Frioui, A. Guezane Lakoud, Existence of solutions for nonlinear fractional integro-differential equations, Advances in Difference Equations, 2020 (1) (2020) 418.
[16] F. Behboudi, A. Razani, M. Oveisiha, Existence of a mountain pass solution for a nonlocal fractional (p, q)-Laplacian problem, Boundary Value Problems, 2020 (1) (2020) 149.
[17] P. Karthikeyan, A. Manikandan, D. Vijay, Some results on ψ-Caputo fractional integro-differential equations, Journal of Fractional Calculus and Applications, 16 (1) (2025) 1–16.
[18] P. Karthikeyan, K. Keerthivasan, Existence of solutions for mixed fractional integro-differential equations in Banach spaces, Discontinuity, Nonlinearity, and Complexity, 15 (3) (2026) 439–450.
[19] A.G. Lakoud, R. Khaldi, A. Kılıc¸man, Existence of solutions for a mixed fractional boundary value problem, Advances in Difference Equations, 2017 (1) (2017) 164.
[20] A. Lachouri, A. Ardjouni, A. Djoudi, Existence and Ulam stability results for fractional differential equations with mixed nonlocal conditions, Azerbaijan Journal of Mathematics, 11 (2) (2021) 78–97.
[21] S. Zibar, B. Tellab, A. Amara, H. Emadifar, A. Kumar, S. Widatalla, Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed φ-Riemann–Liouville and ψ-Caputo fractional derivatives, Boundary Value Problems, 2025 (1) (2025) 8.
[22] M. Murugesan, S.F. Aldosary, H. Gundogdu, Nonlinear sequential Caputo fractional differential systems: existence and Hyers–Ulam stability under coupled mixed boundary constraints, Fractal and Fractional, 10 (3) (2026) 165.
[23] B.H. Rizqan, D. Dhaigude, Nonlinear fractional differential equations with advanced arguments, International Journal of Nonlinear Analysis and Applications, 12 (2) (2021) 1413–1423.
[24] S.A. Murad, A.S. Rafeeq, Existence of solutions of integro-fractional differential equation when α ∈ (2,3] through fixed point theorem, Journal of Mathematical and Computational Science, 11 (5) (2021) 6392–6402.
[25] S.K. Ntouyas, A. Broom, A. Alsaedi, T. Saeed, B. Ahmad, Existence results for a nonlocal coupled system of differential equations involving mixed right and left fractional derivatives and integrals, Symmetry, 12 (4) (2020) 578.
[26] D. O’Regan, Fixed-point theory for the sum of two operators, Applied Mathematics Letters, 9 (1) (1996) 1–8
