Solvability of Multiple Kinds of Fuzzy Fractional Hybrid Differential Equations Using Mnch’s Fixed Point Theorem

Aziz El Ghazouani ¹ ( Department of mathematics, Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco. )
M’hamed Elomari ² ( Department of mathematics, Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco. )

تاریخ ارسال : 1403/09/29 تاریخ تایید : 1403/12/16

کلید واژه: Fractional hybrid differential equations, The measure of non-compactness, Mnch’s fixed-point theorem.,

چکیده مقاله :

The focus of this study is on hybrid differential and fractional hybrid differential equations (HFDEs). Such problems have important applications in a wide range of applied sciences. To address our models, we first study the existence theorem of fuzzy solutions under relatively weaker constraints, combining the measure of noncompactness and Mnch’s fixed-point theorem. The insights provided here extend and refine several previously established findings. Subsequently, two examples are provided to demonstrate the validity of the results obtained.

چکیده انگلیسی :

منابع و مأخذ:

[1] Zadeh LA. Fuzzy sets. Information and control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[2] Chang SSL, Zadeh LA. On fuzzy mapping and control. IEEE transactions on systems, man, and cybernetics. 1972; 1: 30-34. DOI: https://doi.org/10.1109/TSMC.1972.5408553
[3] Dubois D, Prade H. Towards fuzzy differential calculus part 2: Integration on fuzzy intervals. Fuzzy sets and Systems. 1982; 8(2): 105-116. DOI: https://doi.org/10.1016/0165-0114(82)90001-X
[4] Kaleva O. Fuzzy differential equations. Fuzzy sets and systems. 1987; 24(3): 301-317. DOI: https://doi.org/10.1016/0165-0114(87)90029-7
[5] El Ghazouani A, Elomari M. Solving fuzzy non-homogeneous wave equations via laplace residual power series approach. New Mathematics and Natural Computation. 2024: 1-11. DOI: https://doi.org/10.1142/S179300572650002X
[6] El Ghazouani A, Elomari M, Melliani S. Existence and qualitative behavior of mild solutions for fuzzy boundary value problem with nonlocal conditions. Filomat. 2024; 38(21): 7609-7626. DOI: https://doi.org/10.2298/FIL2421609G
[7] El Ghazouani A, Elomari M, Melliani S. Generalized Ulam-Hyer stability results for fuzzy fractional stochastic system under Caputo fractional generalized Hukuhara differentiability concept. Novi Sad Journal of Mathematics. 2024. Accepted. DOI: https://doi.org/10.30755/NSJOM.16819
[8] Kuratowski C. Sur les espaces complets. Fundamenta mathematicae. 1930; 15(1): 301-309. DOI: https://doi.org/10.4064/fm-15-1-301-309
[9] Hilfer R. Applications of fractional calculus in physics. Singapore: World scientific; 2000. DOI: https://doi.org/10.1142/3779
[10] Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. London; elsevier: 1998.
[11] El Ghazouani A, Abdou Amir F, Elomari M, Melliani S. On the existence and uniqueness of fuzzy mild solution of fractional evolution equations. Kragujevac Journal of Mathematics. 2025; 49(6): 949-966. DOI: https://doi.org/10.46793/KgJMat2506.949G
[12] Salahshour S, Allahviranloo T, Abbasbandy S, Baleanu D. Existence and uniqueness results for fractional differential equations with uncertainty. dvances in Difference Equations. 2012; 2012: 1-12. DOI: https://doi.org/10.1186/1687-1847-2012-112
[13] Allahviranloo T, Armand A, Gouyandeh Z. Fuzzy fractional differential equations under generalized fuzzy Caputo derivative. Journal of Intelligent & Fuzzy Systems. 2014; 26(3): 1481-1490. DOI: https://doi.org/10.3233/IFS-130831
[14] Kilbas AA, Srivastava H M, Trujillo JJ. Theory and Applications of Fractional Differential Equations; North-Holland Mathematics Studies. Amsterdam: Elsevier; 2006.
[15] Lakshmikantham V, Leela S, Devi JV. Theory of Fractional Dynamic Systems. Watertown: Cambridge Scientific; 2009.
[16] Lu H, Sun S, Yang D, Teng H. Theory of fractional hybrid differential equations with linear perturbations of second type. Boundary Value Problem. 2013; 23(2013). DOI: https://doi.org/10.1186/1687-2770-2013- 23
[17] Hilal K, Kajouni A. Boundary value problem for hybrid differential equations with fractional order. Advances in Difference Equations. 2015; 2015: 183. DOI: https://doi.org/10.1186/s13662-015-0530-7
[18] Dhage BC. Basic results in the theory of hybrid differential equations with linear perturbations of second type. Tamkang Journal of Mathematics. 2013; 44: 171-186. DOI: https://doi.org/10.5556/j.tkjm.44.2013.1086
[19] Ahmad I, Shah K, Rahman G, Baleanu D. Stability analysis for a nonlinear coupled system of fractional hybrid delay differential equations. Mathematical Methods in the Applied Sciences. 2020; 43: 8669-8682. DOI: https://doi.org/10.1002/mma.6526
[20] Dhage BC. A fixed point theorem in Banach algebras involving three operators with applications. Kyungpook Mathematical Journal. 2004; 44: 145-155.
[29] El Ghazouani A, Abdou Amir F, Elomari M, Melliani S. Fuzzy neutral fractional integro-differential equation existence and stability results involving the Caputo fractional generalized Hukuhara derivative. Journal of Nonlinear, Complex and Data Science. 2024; 25(1): 53-78. DOI: https://doi.org/10.1515/jncds2023-0059
[21] El Ghazouani A, Elomari M, Melliani S. Solvability and GUH stability results of fuzzy nonlinear ABCfractional coupled system. 9th International IFS and Contemporary Mathematics and Engineering Conference, 8-11 July 2023, Tarsus, Turkey. p.20-22.
[22] El Ghazouani A, Talhaoui A, Melliani S. Existence and uniqueness results for a semilinear fuzzy fractional elliptic equation. Filomat. 2023; 37(27): 9315-9326. DOI: https://doi.org/10.2298/FIL2327315G
[23] Abdou Amir F, El Ghazouani A, Melliani S. Fuzzy Fractional Differential Equation Involving the Fuzzy Conformable Derivative and the α-Semigroups. The Scientific World Journal. 2024; 2024(2): 1-11. DOI: https://doi.org/10.1155/2024/9993669
[24] El Ghazouani A, Melliani, S. Existence and Ulam-Hyers stability results to fuzzy fractional boundary value problems via Hilfer fractional derivative. Nonlinear Studies. 2024; 31(3): 759-777.
[25] El Ghazouani A, Abdou Amir F, Elomari M, Melliani S. On the Existence and Uniqueness Results for Fuzzy Fractional Boundary Value Problem Involving Caputo Fractional Derivative. Boletim da Sociedade Paranaense de Matematica. 2024; 42: 1-21. DOI: https://doi.org/10.5269/bspm.65454
[26] Bede B, Stefanini L. Generalized differentiability of fuzzy-valued functions. Fuzzy sets and systems. 2013; 230: 119-141. DOI: https://doi.org/10.1016/j.fss.2012.10.003
[27] Bede B, Gal SG. Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy sets and systems. 2005; 151(3): 581-599. DOI: https://doi.org/10.1016/j.fss.2004.08.001
[28] Salahshour S, Allahviranloo T, Abbasbandy S. Solving fuzzy fractional differential equations by fuzzy Laplace transforms. Communications in Nonlinear Science and Numerical Simulation. 2012; 17(3): 1372- 1381. DOI: https://doi.org/10.1016/j.cnsns.2011.07.005
[29] Bana J. On measures of noncompactness in Banach spaces. Commentationes Mathematicae Universitatis Carolinae. 1980; 21(1): 131-143.
[30] Guo D, Lakshmikantham V, Liu X. Nonlinear integral equations in abstract spaces Berlin: Springer Science & Business Media; 2013. DOI: http://doi.org/10.1007/978-1-4613-1281-9
[31] Mnch H. Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications. 1980; 4(5): 985-999. DOI: https://doi.org/10.1016/0362-546X(80)90010-3

Solvability of Multiple Kinds of Fuzzy Fractional Hybrid Differential Equations Using Mnch’s Fixed Point Theorem

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