Browsing by Author "Alzabut, Jehad"

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A Coupled Nonlinear System of Integro-Differential Equations Using Modified Abc Operator
(World Scientific Publ Co Pte Ltd, 2025) Khan, Hasib; Alzabut, Jehad; Almutairi, D. K.; Alqurashi, Wafa khalaf; Pinelas, Sandra; Tunc, Osman; Azim, Mohammad athar
This paper explores the necessary conditions required for the solutions of an integro-differential system of n-fractional differential equations (n-FDEs) in the modified-ABC case of derivative with initial conditions. The presumed problem is a linearly perturbed system. Some classical fixed point theorems are utilized to derive the solution existence criteria. Additionally, a numerical methodology utilizing Lagrange's interpolation polynomial is developed and implemented in a dynamical framework of a power system for practical applications. In addition, we investigate the properties of Hyers-Ulam's stability and uniqueness. The findings are evaluated using graphical methods to assess the precision and suitability of the approaches
A Fractal-Fractional Covid-19 Model With a Negative Impact of Quarantine on the Diabetic Patients
(Elsevier, 2023) Khan, Hasib; Alzabut, Jehad; Tunc, Osman; Kaabar, Mohammed K. A.
In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal-fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange's interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.
A New Gronwall-Bellman Inequality in Frame of Generalized Proportional Fractional Derivative
(Mdpi, 2019) Alzabut, Jehad; Sudsutad, Weerawat; Kayar, Zeynep; Baghani, Hamid
New versions of a Gronwall-Bellman inequality in the frame of the generalized (Riemann-Liouville and Caputo) proportional fractional derivative are provided. Before proceeding to the main results, we define the generalized Riemann-Liouville and Caputo proportional fractional derivatives and integrals and expose some of their features. We prove our main result in light of some efficient comparison analyses. The Gronwall-Bellman inequality in the case of weighted function is also obtained. By the help of the new proposed inequalities, examples of Riemann-Liouville and Caputo proportional fractional initial value problems are presented to emphasize the solution dependence on the initial data and on the right-hand side.
Riccati Technique for Oscillation of Half-linear/Emden-fowler Neutral Dynamic Equations
(int Scientific Research Publications, 2023) Saker, Samir H.; Sethi, Abhay K.; Tunc, Osman; Alzabut, Jehad
By using the Riccati technique, which reduces the higher order dynamic equations to a Riccati dynamic inequality, we will establish some new sufficient conditions for the oscillation of half-linear/Emden-Fowler neutral dynamic equation of the form (r(rho)((x(rho) + p(rho)x(tau(rho)))(Delta))(gamma))(Delta) + q(rho)x(a)(delta(rho)) + v(rho)x(beta)(eta(rho)) = 0, on a time scale T, where gamma, alpha, and beta are quotients of odd positive integers. An example with particular equation is constructed in consistent to the above equation and oscillation criteria are established for its solution. (c) 2023 All rights reserved.