ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS

Hariharan R; Udhayakumar Ramalıngam

ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

This article explores the controllability of fuzzy fractional differential equations using the Caputo-Katugampola fractional derivative. First, we prove the existence of a mild solution using fractional calculus, fuzzy set theory, semigroup theory, and the Caputo-Katugampola fractional derivative. The main results are obtained through a fixed-point theorem. Finally, we illustrate our findings with an example.

Keywords

Thanks

The authors would like to thank the editor and reviewer for their valuable feedback and suggestions on enhancing the quality of the article.

References

Podlubny, I., (1999), Fractional Differential Equations, Academic Press, San Diego.
Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., (2006), Theory and applications of fractional differential equations, elsevier, 204.
Iskakova, K., Alam, M. M., Ahmad, S., Saifullah, S., Akgül, A. and Yılmaz, G., (2023), Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis, Math. Comput. Simul., 208, pp. 219-245.
Hanif, A., Butt, A. I. K., Ahmad, S., Din, R. U. and Inc, M., (2021), A new fuzzy fractional order model of transmission of Covid-19 with quarantine class, Eur. Phys. J. Plus, 136 (11), pp. 1-28.
Alqahtani, R. T., Ahmad, S. and Akgül, A., (2021), Dynamical analysis of bio-ethanol production model under generalized nonlocal operator in Caputo sense, Mathematics, 9 (19), p. 2370.
Xuan, L., Ahmad, S., Ullah, A., Saifullah, S., Akgül, A. and Qu, H., (2022), Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model, Chaos Solitons Fractals, 159, p. 112113.
Miller K. S. and Ross B., (1993), An Introduction to the Fractional Calculus and Differential Equations, John Wiley & Sons.
Lakshmikantham, V., Leela, S. and Devi, J. V., (2009), Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers.

Zhou, Y., (2013), Basic theory of fractional differential equations, World scientific.
Chang, S. S. and Zadeh, L. A., (1972), On fuzzy mapping and control, IEEE Trans. Syst. Man Cybern., (1), pp. 30-34.
Agarwal, R. P., Lakshmikantham, V. and Nieto, J. J., (2010), On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal. Theory Methods Appl., 72 (6), pp. 2859-2862.
Arshad, S., (2013), On existence and uniqueness of solution of fuzzy fractional differential equations, Iran. J. Fuzzy Syst., 10, pp. 137-151.
Salahshour, S., Allahviranloo, T. and Abbasbandy, S., (2012), Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun. Nonlinear Sci. Numer. Simul., 17 (3), pp. 1372-1381.
Allahviranloo, T., Armand, A. and Gouyandeh, Z., (2014), Fuzzy fractional differential equations under generalized fuzzy Caputo derivative, J. Intell. Fuzzy Syst., 26 (3), pp. 1481-1490.
Katugampola, U. N., (2011), New approach to a generalized fractional integral, Appl. Math. Comput., 218 (3), pp. 860-865.
Katugampola, U. N., (2014), A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., (6), pp. 1-15.
Katugampola, U. N., (2014), Existence and uniqueness results for a class of generalized fractional differential equations, arXiv:1411.5229 [math-ph].
Almeida, R., Malinowska, A. B. and Odzijewicz, T., (2016), Fractional differential equations with dependence on the Caputo-Katugampola derivative, J. Comput. Nonlinear Dyn., 11 (6), 061017.
Zeng, S., Baleanu, D., Bai, Y. and Wu, G., (2017), Fractional differential equations of Caputo-Katugampola type and numerical solutions, Appl. Math. Comput., 315, pp. 549-554.
Baleanu, D., Wu, G. C. and Zeng, S. D., (2017), Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations, Chaos Solitons Fractals, 102, pp. 99-105.
Singh, V., (2019), Controllability of Hilfer fractional differential systems with non-dense domain. Numer. Funct. Anal. Optim., 40 (13), pp. 1572-1592.
Ullah, A., Ullah, A., Ahmad, S., Ahmad, I. and Akgül, A., (2023), On solutions of fuzzy fractional order complex population dynamical model, Numer. Methods Partial Differ. Equ., 39 (6), pp. 4595-4615.
Ahmad, S., Ullah, A., Akgül, A. and Abdeljawad, T., (2021), Semi-analytical solutions of the 3rd order fuzzy dispersive partial differential equations under fractional operators, Alex. Eng. J., 60 (6), pp. 5861-5878.
Zhang, C., Ye, G., Liu, W. and Liu, X., (2024), On controllability for Sobolev-type fuzzy Hilfer fractional integro-differential inclusions with Clarke subdifferential, Chaos Solitons Fractals, 183, 114907.
Ullah, A., Ullah, A., Ahmad, S. and Van Hoa, N., (2023), Fuzzy Yang transform for second order fuzzy differential equations of integer and fractional order, Phys. Scr., 98 (4), p. 044003.
Van Hoa, N., Vu, H. and Duc, T. M., (2019), Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach, Fuzzy Sets Syst., 375, pp. 70-99.
Puri, M. L. and Ralescu, D. A., (1983), Differentials of fuzzy functions, J. Math. Anal. Appl., 91 (2), pp. 552-558.
Hariharan, R. and Udhayakumar, R., (2025), Existence of mild solution for fuzzy fractional differential equation utilizing the Hilfer-Katugampola fractional derivative, Int. J. Optim. Control Theor. Appl., 15 (1), pp. 80-89.
Varun Bose, C. S. and Udhayakumar, R., Velmurugan, S., Saradha, M. and Almarri, B., (2023), Approximate controllability of ψ-Hilfer fractional neutral differential equation with infinite delay, Fractal Fractional, 7 (7), 537.
Zhou, Y., Zhang, L. and Shen, X. H., (2013), Existence of mild solutions for fractional evolution equations, J. Integr. Equ. Appl., 25 (4), pp. 557-586.
Hariharan, R. and Udhayakumar, R., (2024), Approximate Controllability for Fuzzy Fractional Evolution Equations of Order ℓ ∈ (1, 2), Contemp. Math., pp. 3287-3312.

Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems, Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Hariharan R
0009-0009-3258-1878
India

Udhayakumar Ramalıngam ^*
0000-0002-7020-3466
India

Publication Date

January 8, 2026

Submission Date

December 22, 2024

Acceptance Date

April 3, 2025

Published in Issue

Year 2026 Volume: 16 Number: 1

IZ

https://izlik.org/JA82ES35PZ

Cite

RIS / Bibtex

APA

R, H., & Ramalıngam, U. (2026). ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS. TWMS Journal of Applied and Engineering Mathematics, 16(1), 109-122. https://izlik.org/JA82ES35PZ

AMA

1.R H, Ramalıngam U. ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS. JAEM. 2026;16(1):109-122. https://izlik.org/JA82ES35PZ

Chicago

R, Hariharan, and Udhayakumar Ramalıngam. 2026. “ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS”. TWMS Journal of Applied and Engineering Mathematics 16 (1): 109-22. https://izlik.org/JA82ES35PZ.

EndNote

R H, Ramalıngam U (January 1, 2026) ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS. TWMS Journal of Applied and Engineering Mathematics 16 1 109–122.

IEEE

[1]H. R and U. Ramalıngam, “ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS”, JAEM, vol. 16, no. 1, pp. 109–122, Jan. 2026, [Online]. Available: https://izlik.org/JA82ES35PZ

ISNAD

R, Hariharan - Ramalıngam, Udhayakumar. “ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS”. TWMS Journal of Applied and Engineering Mathematics 16/1 (January 1, 2026): 109-122. https://izlik.org/JA82ES35PZ.

JAMA

1.R H, Ramalıngam U. ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS. JAEM. 2026;16:109–122.

MLA

R, Hariharan, and Udhayakumar Ramalıngam. “ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 1, Jan. 2026, pp. 109-22, https://izlik.org/JA82ES35PZ.

Vancouver

1.Hariharan R, Udhayakumar Ramalıngam. ON CONTROLLABILITY RESULTS FOR FUZZY CAPUTO-KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS. JAEM [Internet]. 2026 Jan. 1;16(1):109-22. Available from: https://izlik.org/JA82ES35PZ