Browsing by Author "Khan, Hasib"
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Article Approximate Analytical Solutions of Space-Fractional Telegraph Equations by Sumudu Adomian Decomposition Method(Prairie View A & M Univ, dept Mathematics, 2018) Khan, Hasib; Tunc, Cemil; Khan, Rahmat Ali; Shirzoi, Akhtyar Gul; Khan, AzizThe main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.Article 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 atharThis 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 approachesArticle Existence Theorems and Hyers-Ulam Stability for a Class of Hybrid Fractional Differential Equations With P-Laplacian Operator(Wilmington Scientific Publisher, Llc, 2018) Khan, Hasib; Tunc, Cemil; Chen, Wen; Khan, AzizIn this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with p-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results.Article 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.Article A Fractional Order Zika Virus Model With Mittag?leffler Kernel(Pergamon-elsevier Science Ltd, 2021) Begum, Razia; Tunc, Osman; Khan, Hasib; Gulzar, Haseena; Khan, AzizZika virus is one of the lethal virus which is a threat to humans health. It can be transmitted from human to human, from mosquitos to human, from human to mosquitos. Since there is no vaccine or complete treatment of the Zika viral infection. Therefore, scientists are working on the optimal control strategies. One of the control strategies is the awareness about the spread. In this article, we have presented and analyzed a mathematical model for the Zika virus and have checked the results on long time. The model has closer results to the classical based on our numerical scheme by the help of Lagrange's interpolation polynomial. (c) 2021 Elsevier Ltd. All rights reserved.Article A Generalization of Minkowski's Inequality by Hahn Integral Operator(Taylor & Francis Ltd, 2018) Khan, Hasib; Tunc, Cemil; Alkhazan, Abdulwasea; Ameen, Barakat; Khan, AzizIn this paper, we use the Hahn integral operator for the description of new generalization of Minkowski's inequality. The use of this integral operator definitely generalizes the classical Minkowski's inequality. Our results with this new integral operator have the abilities to be utilized for the analysis of many mathematical problems as applications of the work.Conference Object Green Function's Properties and Existence Theorems for Nonlinear Singular-Delay Differential Equations(Amer inst Mathematical Sciences-aims, 2020) Khan, Hasib; Tunc, Cemil; Khan, AzizIn this paper, we are dealing with singular fractional differential equations (DEs) having delay and U-p (p-Laplacian operator). In our problem, we Contemplate two fractional order differential operators that is Riemann-Liouville and Caputo's with fractional integral and fractional differential initial boundary conditions.The SFDE is given by {D-gamma[U*(p)[D(kappa)x(t)]] + Q(t)zeta(1)(t, x(t - e*)) = 0, T-0(1)-gamma(U-p*[D(kappa)x(t)]]t=0 = 0 =T02-gamma(Up*[D kappa x(t)]]vertical bar t=0, D-delta* x(1) = 0, x(1) = x'(0), x((k)) (0) = 0 for k = 2, 3, ..., n-1, zeta 1 is a continuous function and singular at t and x(t) for some values of t 2 [0; 1]. The operator D-gamma is Riemann{Liouville fractional derivative while D delta*;D-kappa stand for Caputo fractional derivatives and delta*, gamma is an element of(1, 2], n - 1 < kappa <= n; where n >= 3. For the study of the EUS, fixed point approach is followed in this paper and an application is given to explain the findings.Article Inequalities for N-Class of Functions Using the Saigo Fractional Integral Operator(Springer-verlag Italia Srl, 2019) Khan, Hasib; Tunc, Cemil; Baleanu, Dumitru; Khan, Aziz; Alkhazzan, AbdulwaseaThe role of fractional integral operators can be found as one of the best ways to generalize the classical inequalities. In this paper, we use the Saigo fractional integral operator to produce some inequalities for a class of n-decreasing positive functions. The results are more general than the available classical results in the literature.Article Mathematical Analysis of Stochastic Epidemic Model of Mers-Corona & Application of Ergodic Theory(Elsevier, 2023) Hussain, Shah; Tunc, Osman; Rahman, Ghaus Ur; Khan, Hasib; Nadia, ElissaThe "Middle East Respiratory" (MERS-Cov) is among the world's dangerous diseases that still exist. Presently it is a threat to Arab countries, but it is a horrible prediction that it may propagate like COVID-19. In this article, a stochastic version of the epidemic model, MERS-Cov, is presented. Initially, a mathematical form is given to the dynamics of the disease while incorporating some unpredictable factors. The study of the underlying model shows the existence of positive global solution. Formulating appropriate Lyapunov functionals, the paper will also explore parametric conditions which will lead to the extinction of the disease from a community. Moreover, to reveal that the infection will persist, ergodic stationary distribution will be carried out. It will also be shown that a threshold quantity exists, which will determine some essential parameters for exploring other dynamical aspects of the main model. With the addition of some examples, the underlying stochastic model of MERS-Cov will be studied graphically for more illustration.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.Article Minkowski's Inequality for the Ab-Fractional Integral Operator(Springer, 2019) Khan, Hasib; Abdeljawad, Thabet; Tunc, Cemil; Alkhazzan, Abdulwasea; Khan, AzizRecently, AB-fractional calculus has been introduced by Atangana and Baleanu and attracted a large number of scientists in different scientific fields for the exploration of diverse topics. An interesting aspect is the generalization of classical inequalities via AB-fractional integral operators. In this paper, we aim to generalize Minkowski inequality using the AB-fractional integral operator.Article On Fractal-Fractional Covid-19 Mathematical Model(Pergamon-elsevier Science Ltd, 2022) Khan, Hasib; Ahmad, Farooq; Tunc, Osman; Idrees, MuhammadIn this article, we are studying a Covid-19 mathematical model in the fractal-fractional sense of operators for the existence of solution, Hyers-Ulam (HU) stability and computational results. For the qualitative analysis, we convert the model to an equivalent integral form and investigate its qualitative analysis with the help of iterative convergent sequence and fixed point approach. For the computational aspect, we take help from the Lagrange's interpolation and produce a numerical scheme for the fractal-fractional waterborne model. The scheme is then tested for a case study and we obtain interesting results.(c) 2022 Published by Elsevier Ltd.Article Stability Results and Existence Theorems for Nonlinear Delay-Fractional Differential Equations With Φ*p-Operator(Wilmington Scientific Publisher, Llc, 2020) Khan, Hasib; Tunc, Cemil; Khan, AzizThe study of delay-fractional differential equations (fractional DEs) have recently attracted a lot of attention from scientists working on many different subjects dealing with mathematically modeling. In the study of fractional DEs the first question one might raise is whether the problem has a solution or not. Also, whether the problem is stable or not? In order to ensure the answer to these questions, we discuss the existence and uniqueness of solutions (EUS) and Hyers-Ulam stability (HUS) for our proposed problem, a nonlinear fractional DE with p-Laplacian operator and a non zero delay tau > 0 of order n - 1 < nu*, epsilon < n, for n >= 3 in Banach space A. We use the Caputo's definition for the fractional differential operators D-nu*, D-epsilon. The assumed fractional DE with p-Laplacian operator is more general and complex than that studied by Khan et al. Eur Phys J Plus, (2018);133:26.