NONE 20260102084800058 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON MATHEMATICS 1109-2769 2224-2880 Hassan Al-Zoubi Department of Mathematics, Al-Zaytoonah University, Queen Alia Airport St 594, Amman 11733, JORDAN Hamza Alzaareer Department of Mathematics, Al-Zaytoonah University, Queen Alia Airport St 594, Amman 11733, JORDAN 01 02 2026 01 02 2026 1 1 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/23206.2026.25.1 https://wseas.com/journals/mathematics/2026/a025106-001(2026).pdf R. H. Fox, On topologies for function spaces, Bull. AMS 51 (1945). J. L. Kelley, General Topology, Springer (1955). E. Spanier, Algebraic Topology, McGraw-Hill (1966). M. W. Hirsch, Differential Topology, Springer (1976). R. S. Hamilton, The inverse function theorem, Bull. AMS 7 (1982). A. Kriegl and P. W. Michor, The convenient setting of global analysis, American Mathematical Society, Providence, RI, 1997. J. Milnor, Construction of universal bundles. I, Ann. of Math. (2) 63 (1956), 272–284. H. Omori, Infinite-Dimensional Groups, Springer (1974). A. Pressley and G. Segal, Loop Groups, Oxford (1986). P. Michor, Manifolds of Mappings, Shiva (1980). H. Glöckner, Exponential laws for ultrametric partially differentiable functions and applications, P-Adic Num Ultrametr Anal Appl. 5 (2013), 122–159. H. Alzaareer, Lie group structures on groups of maps on non-compact spaces and manifolds, Ph.D. Thesis, Paderborn (2013). H. Glöckner, Infinite-dimensional Lie groups without completeness restrictions, In: Geometry and Analysis on Lie Groups, Banach Center Publ. 55, Polish Acad. Sci., Warsaw, 2002, pp. 43–59. H. H. Keller, Differential Calculus in Locally Convex Spaces, Lecture Notes in Mathematics, vol. 417, Springer-Verlag, Berlin, 1974. J. Milnor, Remarks on infinite-dimensional Lie groups, in: Relativité, Groupes et Topologie II, B. S. DeWitt and R. Stora (Eds.), North-Holland, Amsterdam, 1984, pp. 1007–1057. H. Glöckner and K.-H. Neeb, Infinite-dimensional Lie Groups. General Theory and Main Examples, Reprint ed., Graduate Texts in Mathematics, vol. 274, Springer, New York, 2017. ISBN: 038709444X, 9780387094441. 350 pp. H. Alzaareer, Lie groups of C k -maps on non-compact manifolds and the fundamental theorem for Lie group-valued mappings, J. Group Theory, vol. 24, no. 6, pp. 1099–1134, 2021. M. Mhailan et al., On fractional vector analysis, J. Math. Comput. Sci. 10, 2320–2326 (2020). I. Batiha et al., Tuning the fractional-order PID-controller for blood glucose, Int. J. Adv. Soft Comput. Appl. 13(2), 1–10 (2021). I. Batiha et al., Design fractional-order PID controller for robot arm, Int. J. Adv. Soft Comput. Appl. 14(2), 96–114 (2022).