Browsing by Author "Alzabut, J."

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New Results on the Existence of Periodic Solutions for Rayleigh Equations With State-Dependent Delay
(Walter de Gruyter GmbH, 2022) Eswari, R.; Alzabut, J.; Samei, M.E.; Tunç, C.; Jonnalagadda, J.M.
We consider a Rayleigh-type equation with state-dependent delay. We establish a set of new suficient conditions on the existence of at least one positive periodic solution by using the continuation theorem of coincidence degree theory. Our results not only provide a new approach but also generalize previous results. An example with graphical representations are presented to illustrate the results. © 2022 Rajendiran Eswari et al., published by De Gruyter.
On System of Nonlinear Coupled Differential Equations and Inclusions Involving Caputo-Type Sequential Derivatives of Fractional Order
(Taylor & Francis Ltd, 2022) Subramanian, M.; Manigandan, M.; Tunc, C.; Gopal, T. N.; Alzabut, J.
We investigate a new class of boundary value problems of a nonlinear coupled system of sequential fractional differential equations and inclusions involving Caputo fractional derivatives and boundary conditions. We use standard fixed-point theory tools to deduce sufficient criteria for the existence and uniqueness of solutions to the problems at hand. Examples are discussed to illustrate the validity of the proposed results.
On System of Variable Order Nonlinear P-Laplacian Fractional Differential Equations With Biological Application
(MDPI, 2023) Khan, H.; Alzabut, J.; Gulzar, H.; Tunç, O.; Pinelas, S.
The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo’s fractional derivative. We investigate the existence of solutions and the Hyers–Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations. © 2023 by the authors.