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Fractional order nonlinear random differential equation in separable Banach algebra | ||
| Journal of Hyperstructures | ||
| دوره 15، شماره 1، شهریور 2026، صفحه 112-122 اصل مقاله (1.62 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2026.17768.1107 | ||
| نویسندگان | ||
| Kalpana D Jagtap* 1؛ Bhalchandra D Karande2 | ||
| 1Department of Mathematics, Dayanad Science College, Latur | ||
| 2Department of Mathematics, Maharashtra Udaygiri Mahavidyalaya, Udgir (413517). | ||
| چکیده | ||
| This paper investigates fractional-order differential equations with random operators in a separable Banach algebra. The main goal is to prove the existence of random solutions for these equations. We focus on an initial value problem involving fractional order differential equations with random operators. By transforming this initial value problem into an equivalent integral form and applying the fixed point theorem along with the Caratheodory condition, we formulate some hypothesis for the existence of random solutions. Additionally, we demonstrate that these random solutions possess local attractivity. This study provides a framework for understanding and solving existence of random solutions for fractional order differential equations with random operators. An illustrative example is also provided to verify and demonstrate the applicability of the main result. | ||
| کلیدواژهها | ||
| Fractional differential equation؛ fixed point theorem؛ random solu- tions؛ random integral equations؛ initial value problem | ||
| مراجع | ||
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[1] Said Abbas, Nassir Al Arifi, Mouffak Benchohra, and Yong Zhou. Random coupled hilfer and hadamard fractional differential systems in generalized banach spaces, Mathematics, 7(3),285 (2019), 2-15. [2] Ali Akg¨ul and SarbazH.A. Khoshnaw, Application of fractional derivative on non-linear biochemical reaction models, International Journal of Intelligent Networks,1 (2020), 52-58. [3] AAM Arafa, Fractional differential equations in description of bacterial growth, Differential Equations and Dynamical Systems, 21 (2013), 205-214. [4] Ramendra Bose, Some random fixed point theorems concerning three random operators on a banach algebra, International Journal of Pure and Applied Mathematics, 45(3) (2008), 453-462. [5] BC Dhage, Random fixed point theorems in banach algebras with applications to random integral equations, Tamkang journal of Mathematics, 34(1) (2003), 29-43. [6] Bapurao C Dhage and Sotiris K Ntouyas, Existence and attractivity results for nonlinear first order random differential equations, Opuscula Mathematica, 30(4) (2010), 411-429. [7] Bhalchandra Dasarao Karande, Existence of uniform global locally attractive solutions for fractional order nonlinear random integral equation, Journal of Global Research in Mathematical Archives (JGRMA), 1(8), (2013), 34-43. [8] Srinivasan Madhumitha, Tharmalingam Gunasekar, Ammar Alsinai, Prabakaran Raghavendran, and Read S. A. Qahtan, Existence and controllability for second-order functional differential equations with infinite delay and random effects, International Journal of Differential Equations, 2024 (2004), 1-9. [9] FC Meral, TJ Royston, and R Magin, Fractional calculus in viscoelasticity: an experimental study, Communications in nonlinear science and numerical simulation, 15(4) (2010), 939-945. [10] Farukh Ahmed Mulani, Review on various applications of fractional calcu- lus in science, International Education and Research Journal (IERJ), 9(5) (2023), 63-64. [11] Martina Pavlaˇckov´a and Valentina Taddei, Mild solutions of second-order semilinear impulsive differential inclusions in banach spaces, Mathematics, 10(4) (2022), 2-25. [12] Neetu Vishwakarma, Common random fixed point theorem for compatible random multivalued operators, IOSR Journal of Mathematics, 3 (2012), 39-43. | ||
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