Browsing by Author "Khan, Aziz"

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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, Aziz
The 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.
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, Aziz
In 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.
A Fractional Order Zika Virus Model With Mittag?leffler Kernel
(Pergamon-elsevier Science Ltd, 2021) Begum, Razia; Tunc, Osman; Khan, Hasib; Gulzar, Haseena; Khan, Aziz
Zika 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.
A Generalization of Minkowski's Inequality by Hahn Integral Operator
(Taylor & Francis Ltd, 2018) Khan, Hasib; Tunc, Cemil; Alkhazan, Abdulwasea; Ameen, Barakat; Khan, Aziz
In 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.
Green Function's Properties and Existence Theorems for Nonlinear Singular-Delay Differential Equations
(Amer inst Mathematical Sciences-aims, 2020) Khan, Hasib; Tunc, Cemil; Khan, Aziz
In 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.
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, Abdulwasea
The 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.
Minkowski's Inequality for the Ab-Fractional Integral Operator
(Springer, 2019) Khan, Hasib; Abdeljawad, Thabet; Tunc, Cemil; Alkhazzan, Abdulwasea; Khan, Aziz
Recently, 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.
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, Aziz
The 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.