In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained results.

- Gaul, L., Klein, P. & Kemple, S. (1991). Damping description involving fractional operators. Mechanical Systems and Signal Processing, 5, 81-88.
- Glockle, W. G., Nonnenmacher, T. F. (1995). A fractional calculus approach to self-semilar protein dynamics. Biophysical Journal, 68(1), 46-53.
- Metzler, R., Schick, W., Kilian, H. G., & Nonnenmacher, T. F. (1995). Relaxation in filled poly- mers: a fractional calculus approach. The Journal of Chemical Physics, 103, 7180-7186.
- Scher, H., Montroll, E. W. (1975). Anomalous transit time dispersion in amorphous solids. Physical Review B, 12, 2455-2477.
- Anbalagan, P., Ramachandran, R., Alzabut, J., Hincal, E. & Niezabitowski, M. (2022). Improved results on finite-time passivity and synchronization problem for fractional-order memristor-based competitive neural networks: interval matrix approach. Fractal and Fractional, 6(1), 1-36.
- Diethelm, K., Ford, N. J. (2002). Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265, 229-248.
- Joseph, D., Raja, R., Alzabut, J., Niezabitowski, M., Selvam, A. G. M. & Bagdasar, O. O. (2021). An LMI approach based mathematical model to Control Aedes Aegypti mosquitoes population via biological control. Mathematical Problems in Engineering, 2021, Article ID 5565949, 1-18. https://doi.org/10.1155/2021/556599
- Khuddush, M., Prasad, K. R. (2023). Existence, uniqueness and stability analysis of a tempered fractional order thermistor boundary value problems. Journal of Analysis, 31, 85-107. https://doi.org/10.1007/s41478-022-00438-6
- Khuddush, M., Prasad, K. R. & Leela. D. (2022). Existence of solutions to the infinity-point Fractional BVP posed on half-line via a family of measure of noncompactness in the Holder Space Cl,(R+). Filomat, 36(10), 3527-3543. https://doi.org/10.2298/FIL2210527K
- Khuddush, M., Prasad, K. R. & Veeraiah, P. (2022). Infinitely many positive solutions for an iterative system of fractional BVPs with multistrip Riemann–Stieltjes integral boundary conditions. Afrika Matematika, 33, 91. https://doi.org/10.1007/s13370-022-01026-4
- Khuddush, M., Kathun, S. (2023). Infinitely many positive solutions and Ulam–Hyers stability of fractional order two-point boundary value problems. Journal of Analysis. https://doi.org/10.1007/s41478-023-00549-8
- Kilbas, A. A., Marzan, S. A. (2005). Nonlinear differential equation with the Caputo fraction derivative in the space of continuously differentiable functions. Differential Equations, 41, 84-89.
- Podlubny, L. (1999). Fractional differential equations, Academic Press, New York.
- Pratap, A., Raja, R., Cao, C., Alzabut, J. & Huang, C. (2020). Finite-time synchronization criterion of graph theory perspective fractional order coupled discontinuous neural networks. Advances in Difference Equations 2020, 97. https://doi.org/10.1186/s13662-020-02551-x
- Seemab, S., Feckan, M., Alzabut, J. & Abbas, S. (2021). On the existence and Ulam-Hyers stability of a new class of partial fractional differential equations with impulses. Filomat, 35(6), 1977-1991.
- Shah, K., Abdeljawad1, T., Abdalla, B. & Abualrub, M. (2022). Utilizing fixed point approach to investigate piecewise equations with nonsingular type derivative. AIMS Mathematics, 7(8), 14614– 14630.
- Shah, K., Arfan, M., Ullah, A., Al-Mdallal, Q., Ansari, K. J. & Abdeljawad, T. (2022). Computational study on the dynamics of fractional order differential equations with applications. Chaos, Solitons & Fractals,, 157, 111955. https://doi.org/10.1016/j.chaos.2022.111955
- Victor, D. W. J., Khuddush, M. (2022). Existence of solutions for n-dimensional fractional order BVP with infinity–point boundary conditions via the concept of measure of noncompactness. Advanced Studies: Euro-Tbilisi Mathematical Journal, 15(1), 19–37. https://doi.org/10.32513/asetmj/19322008202
- Dhage, B. C. (2004). A nonlinear alternative in Banach algebras with applications to functional differential equations. Nonlinear Functional Analysis and Applications, 8, 563-575.
- Dhage, B. C. (2005). On a fixed point theorem in Banach algebras with applications. Applied Mathematics Letters, 18(3), 273-280.
- Dhage, B. C., Jadhav, N. (2013). Basic results in the theory of hybrid differential equations with linear perturbations of second type. Tamkang Journal of Mathematics, 44(2), 171-186.
- Ali, A., Shah, K. & Khan, R. A. (2017). Existence of solution to a coupled system of hybrid fractional differential equations, Bulletin of Mathematical Analysis and Applications, 9(1), 9-18.
- Alzabut, J., Selvam, A. G. M., Vignesh, D. & Gholami, Y. (2021). Solvability and stability of nonlinear hybrid ?-difference equations of fractional-order. International Journal of Nonlinear Sciences and Numerical Simulation, 2021. https://doi.org/10.1515/ijnsns-2021-0005
- Baleanu, D., Etemad, S., Pourrazi, S. & Rezapour, S. (2019). On the new fractional hybrid boundary value problems with three-point integral hybrid conditions. Advances in Difference Equations, 473, 1-21.
- Buvaneswari, K., Karthikeyan, P. & Baleanu, D. (2020). On a system of fractional coupled hybrid Hadamard differential equations with terminal conditions. Advances in Difference Equations, 419, 1-12.
- Herzallah, M. A. E., Baleanu, D. (2014). On fractional order hybrid differential equations. Abstract and Applied Analysis, 2014, 1-8.
- Houas, M. (2021). Existence and stability results for hybrid fractional q? differential pantograph equations. Asia Mathematika, 5(2), 20-35.
- Houas, M. (2018). Solvability of a system of fractional hybrid differential equations. Communications in Optimization Theory, Article ID 12, 1- 9. https://doi.org/10.23952/cot.2018.12
- Nazir, G., Shah, K., Abdeljawad, T., Khalil, H. & and Khan, R. A. (2020). A prior estimate method to investigate sequential hybrid fractional differential equations. Fractals, 28(8), 1-12.
- Baitiche, Z., Guerbati, K., Benchohra, M. & Henderson, J. (2020). Boundary value problems for hybrid caputo sequential fractional differential equations. Communications on Applied Nonlinear Analysis, 4, 1-16.
- Jamil, M., Khan, R. A. & Shah, K. (2019). Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations. Boundary Value Problems, 2019: 77, 1-12.
- Khan, H., Alshehri, H. M. & Khan, Z. A. (2021). A fractional-order sequential hybrid system with an application to a biological system. Complexity, 2021, Article ID 2018307, 1-9.
- Khan, R. A., Gul, S., Jarad, F. & Khan, H. (2021). Existence results for a general class of sequential hybrid fractional differential equations. Advances in Difference Equations, 2021, 284, 1- 14.
- Prasad, K. R., Khuddush, M. & Leela, D. (2021). Existence of solutions for n?dimensional fractional order hybrid BVPs with integral boundary conditions by an application of n?fixed point theorem. The Journal of Analysis, 29(3), 963-985.
- Dhage, B. C., Lakshmikantham, V. (2010). Basic results on hybrid differential equations. Nonlinear Analysis: Hybrid Systems, 4(3), 414-424.
- Zhao, Y, Sun, S., Hana, Z. & Li, Q. (2011). Theory of fractional hybrid differential equations. Computers & Mathematics with Applications. 62(3), 1312-1324.
- Ahmad, B., Ntouyas, S. K. & Alsaedi, A. (2014). Existence results for a system of coupled hybrid fractional differential equations. The Scientific World Journal, 2014. Article ID 426438, 1-7.
- Kilbas, A. A., Srivastava, H. M. & Trujillo, J. J. (2006). Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204, Elsevier Science B. V., Amsterdam.
- Granas, A., Dugundji, J. (2003). Fixed Point Theory. Springer, New York, NY, USA.
- Ahmad, B., Ntouyas, S. K. (2015). Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions. Applied Mathematics and Computation, 266, 615-622.

**ISSN:**2146-0957**Yayın Aralığı:**4**Yayıncı:**Prof. Dr. Ramazan YAMAN

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