Geometric process solving a class of analytic functions using q-convolution differential operator

References

• Koornwinder TH. q-Special functions, an overview. arXiv preprint math/0511148. 2005.
   Google Scholar
• Carmichael RD. The general theory of linear q-difference equations. Am J Math. 1912;34:147–168. doi: 10.2307/2369887
   Google Scholar
• Jackson FH. On q-definite integrals. Quart J Pure Appl Math. 1910;41:193–203.
   Google Scholar
• Mason TE. On properties of the solution of linear q-difference equations with entire function coefficients. Am J Math. 1915;37:439–444. doi: 10.2307/2370216
   Google Scholar
• Trjitzinsky WJ. Analytic theory of linear q-difference equations. Acta Math. 1933;61:1–38. doi: 10.1007/BF02547785
   Google Scholar
• Ismail MEH, Merkes E, Styer D. A generalization of starlike functions. Complex Var Theory Appl. 1990;14:77–84.
   Google Scholar
• Sàlàgean GS. Subclasses of univalent functions. In: Complex analysis-fifth Romanian-Finnish seminar, part 1 (Bucharest, 1981). Berlin: Springer; 1983. p. 362–372. (Lecture notes in mathematics; 1013).
   Google Scholar
• Al-Oboudi FM. On univalent functions defined by a generalized Sàlàgean operator. Int J Math Math Sci. 2004;2004(27):1429–1436. doi: 10.1155/S0161171204108090
   Google Scholar
• Ibrahim RW, Darus M. Univalent functions formulated by the Sàlàgean-difference operator. Int J Anal App. 2019;17(4):652–658.
   Google Scholar
• Naeem M, et al. A new subclass of analytic functions defined by using Salagean q-differential operator. Mathematics. 2019;7(5):458. doi: 10.3390/math7050458
   Web of Science ®Google Scholar
• El-Qadeem AH, Mamon MA. Comprehensive subclasses of multivalent functions with negative coefficients defined by using a q-difference operator. Tran A Razmadze Math Ins. 2018;172(3):510–526. doi: 10.1016/j.trmi.2018.04.002
   Web of Science ®Google Scholar
• Duren P. Univalent functions. New York: Springer-Verlag, Inc; 1983. (Grundlehren der mathematischen Wissenschaften; 259).
   Google Scholar
• Miller SS, Mocanu PT. Differential subordinations: theory and applications. Tbilisi, Georgia: CRC Press; 2000.
   Google Scholar
• Ibrahim RW. Arched foot based on conformal complex neural network testing. Math Comput Simul. 2020;174:175–182. doi: 10.1016/j.matcom.2020.02.016
   Web of Science ®Google Scholar
• Ibrahim RW. Conformal geometry of the turtle shell. J King Saud Univ Sci. 2020;32:2202–2206. doi: 10.1016/j.jksus.2020.02.024
   Web of Science ®Google Scholar
• Govindaraj M, Sivasubramanian S. On a class of analytic functions related to conic domains involving q-calculus. Anal Math. 2017;43:475–487. doi: 10.1007/s10476-017-0206-5
   Web of Science ®Google Scholar
• Shang Y. Vulnerability of networks: fractional percolation on random graphs. Phys Rev E. 2014;89:012813. doi: 10.1103/PhysRevE.89.012813
   Google Scholar
• Shang Y. False positive and false negative effects on network attacks. J Stat Phys. 2018;170:141–164. doi: 10.1007/s10955-017-1923-7
   Web of Science ®Google Scholar
• Dziok J. Inclusion relationships between classes of functions defined by subordination. Ann Polonici Math. 2011;100:193–202. doi: 10.4064/ap100-2-8
   Web of Science ®Google Scholar
• Ruscheweyh S, Sheil-Small T. Hadamard products of schlicht functions and the Póyla-Schoenberg conjecture. Comment Math Helv. 1973;48:119–135. doi: 10.1007/BF02566116
   Web of Science ®Google Scholar
• Littlewood JE. On inequalities in the theory of functions. Proc Lond Math Soc. 1925;23:481–519. doi: 10.1112/plms/s2-23.1.481
   Google Scholar
• Arnold BC. Majorization and the Lorenz order: a brief introduction. Vol. 43. Berlin: Springer-Verlag; 1987.
   Google Scholar
• Ruscheweyh S. Convolutions in geometric function theory. Montréal, Montreal, Que: Presses Univ.; 1982.
   Google Scholar
• Ibrahim RW, Maslina D. Analytic study of complex fractional Tsallis' entropy with applications in CNNs. Entropy. 2018;20(10):722. doi: 10.3390/e20100722
   Web of Science ®Google Scholar
• Ibrahim RW, Meshram C, Hadid SB. Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator. J Ocean Eng Sci. 2020;5(2):186–195. doi: 10.1016/j.joes.2019.11.001
   Web of Science ®Google Scholar
• Ibrahim RW, Jahangiri JM. Conformable differential operator generalizes the Briot-Bouquet differential equation in a complex domain. AIMS Math. 2019;4(6):1582–1595. doi: 10.3934/math.2019.6.1582
   Web of Science ®Google Scholar
• Miller SS, Mocanu PT. Marx-Strohhäcker differential subordination systems. Proc Amer Math Soc. 1987;99(3):527–534.
   Web of Science ®Google Scholar
• Marx A. Unteruchungen iiber schlicht Abbildungen. Math Ann. 1932/33;107:40–67. doi: 10.1007/BF01448878
   Google Scholar
• Seadawy AR, Lu D, Yue C. Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability. J Taibah Univ Sci. 2017;11(4):623–633. doi: 10.1016/j.jtusci.2016.06.002
   Web of Science ®Google Scholar
• Seadawy AR, Iqbal M, Lu D. Nonlinear wave solutions of the Kudryashov-Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity. J Taibah Univ Sci. 2019;13(1):1060–1072. doi: 10.1080/16583655.2019.1680170
   Web of Science ®Google Scholar
• Lu D, Seadawy AR, Ali A. Applications of exact traveling wave solutions of modified Liouville and the symmetric regularized long wave equations via two new techniques. Res Phys. 2018;9:1403–1410.
   Google Scholar
• Lu D, Seadawy AR, Ali A. Dispersive traveling wave solutions of the equal-width and modified equal-width equations via mathematical methods and its applications. Res Phys. 2018;9:313–320.
   Google Scholar
• Ali A, Seadawy AR, Lu D. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications. Open Phys. 2018;16:219–226. doi: 10.1515/phys-2018-0032
   Web of Science ®Google Scholar
• Ali A, Seadawy AR, Lu D. New solitary wave solutions of some nonlinear models and their applications. Adv Differ Equ. 2018;2018:232. doi: 10.1186/s13662-018-1687-7
   Google Scholar
• Ali A, Seadawy AR, Baleanu D. Propagation of harmonic waves in a cylindrical rod via generalized Pochhammer-Chree dynamical wave equation. Res Phys. 2020;17:103039.
   Google Scholar
• Seadawy AR, Ali A, Albarakati WA. Analytical wave solutions of the (2+1)-dimensional first integro-differential Kadomtsev-Petviashivili hierarchy equation by using modified mathematical methods. Res Phys. 2019;15:102775.
   Google Scholar