http://hdl.handle.net/20.500.12416/412 Matematik Bölümü yayınlarını içerir. Wed, 28 Oct 2026 16:18:47 GMT 2026-10-28T16:18:47Z http://hdl.handle.net/20.500.12416/8524 SOME SYMMETRIC PROPERTIES AND APPLICATIONS OF WEIGHTED FRACTIONAL INTEGRAL OPERATOR Wu, Shanhe; Samraiz, Muhammad; Mehmood, Ahsan; Jarad, Fahd; Naheed, Saima In this paper, a weighted generalized fractional integral operator based on the Mittag-Leffler function is established, and it exhibits symmetric characteristics concerning classical operators. We demonstrate the semigroup property as well as the boundedness of the operator in absolute continuous like spaces. In this work, some applications with graphical representation are also considered. Finally, we modify the weighted generalized Laplace transform and then applied it to the newly defined weighted fractional integral operator. The defined operator is an extension and generalization of classical Riemann-Liouville and Prabhakar integral operators. Sun, 01 Jan 2023 00:00:00 GMT http://hdl.handle.net/20.500.12416/8524 2023-01-01T00:00:00Z http://hdl.handle.net/20.500.12416/8523 Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation Saifullah, Sayed; Alqarni, M.M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E. We investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct a comprehensive analysis, we employ the Generalized Kudryashov Technique (KT), Modified KT, and the sine–cosine method. Through the application of these advanced methods, a diverse range of traveling wave solutions is derived, encompassing both bounded and singular types. Among these solutions are dark and bell-shaped waves, as well as periodic waves. Significantly, our investigation reveals novel solutions that have not been previously documented in existing literature. These findings present novel contributions to the field and offer potential applications in various physical phenomena, enhancing our understanding of nonlinear wave equations. Fri, 01 Sep 2023 00:00:00 GMT http://hdl.handle.net/20.500.12416/8523 2023-09-01T00:00:00Z http://hdl.handle.net/20.500.12416/8522 Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method Chaudhary, Rahul; Aeri, Shivani; Bala, Anu; Kumar, Rakesh; Baleanu, Dumitru Vieta-Lucas polynomials (VLPs) belong to the class of weighted orthogonal polynomials, which can be used to effectively handle various natural and engineered problems. The classical fractional derivative due to Caputo is used to write the emerging operational matrices. These matrices are developed and evaluated by using the properties of VLPs. The residuated functions are mapped to zero by the tools of the Tau algorithm. Convergence and error analysis are thoroughly explored. Test examples for a fractional system of differential equations are borrowed from literature. The theoretical and simulated exercise on these examples authenticate the relevance of this scheme. Here, novel inclusion of Vieta-Lucas polynomials has been ensured in combination with the Tau approach. The operational matrix approach which provides extensive information about the fractional derivatives of different terms of Vieta-Lucas polynomial expansion, is ensured to operate to reduce the problem into an algebraic setup. The novelty is further enhanced by comparing the present scheme with the fourth-order Runge–Kutta method. Thu, 01 Feb 2024 00:00:00 GMT http://hdl.handle.net/20.500.12416/8522 2024-02-01T00:00:00Z http://hdl.handle.net/20.500.12416/8521 Solving fractional integro-differential equations by Aboodh transform Raghavendran, Prabakaran; Gunasekar, Tharmalingam; Balasundaram, Hemalatha; Santra, Shyam Sundar; Majumder, Debasish; Baleanu, Dumitru This study approaches some families of fractional integro-differential equations (FIDEs) using a simple fractional calculus method, which leads to several appealing consequences, including the classical Frobenius method, which is generalized. The method presented here is based mostly on certain general theorems on particular solutions of FIDEs using the Aboodh transform and binomial series extension coefficients. We additionally demonstrate techniques to solve FIDEs. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/20.500.12416/8521 2024-01-01T00:00:00Z