Browsing by Author "Khan, Hasib"

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Citation - WoS: 2
Citation - Scopus: 1
A fixed point theorem on multiplicative metric space with integral-type inequality
(Journal Mathematics & Computer Science-jmcs, 2018) Khan, Aziz; Baleanu, Dumitru; Khan, Hasib; Baleanu, Dumitru; Jafari, Hossein; Khan, Tahir Saeed; Alqurashi, Maysaa; 56389; Matematik
In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (X, triangle) by the help of integral-type contractions of self-quadruple mappings (SQMs), i.e., for p(1), p(2), p(3), p(4) : X -> R. For this, we assume that the SQMs are weakly compatible mappings and the pairs (p(1), p(3)) and (p(2), p(4)) satisfy the property (CLRp3p4). Further, two corollaries are produced from our main theorem as special cases. The novelty of these results is that for the unique common fixed point (CFP) of the SQMs p(1), p(2), p(3), p(4), we do not need to the assumption of completeness of the MMS (X, triangle). These results generalize the work of Abdou, [A. A. N. Abdou, J. Nonlinear Sci. Appl., 9 (2016), 2244-2257], and many others in the available literature.
Citation - WoS: 54
Citation - Scopus: 81
A Modification Fractional Variational Iteration Method For Solving Non-Linear Gas Dynamic and Coupled Kdv Equations Involving Local Fractional Operators
(Vinca inst Nuclear Sci, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Jassim, Hassan Kamil; Khan, Hasib; 56389; Matematik
In this paper, we apply a new technique, namely local fractional variational iteration transform method on homogeneous/non-homogeneous non-linear gas dynamic and coupled KdV equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative and integral operators. This method is the combination of the local fractional Laplace transform and variational iteration method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Citation - WoS: 75
Citation - Scopus: 80
A Singular Abc-Fractional Differential Equation With P-Laplacian Operator
(Pergamon-elsevier Science Ltd, 2019) Jarad, Fahd; Khan, Hasib; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Khan, Aziz; 234808; Matematik
In this article, we have focused on the existence and uniqueness of solutions and Hyers-Ulam stability for ABC-fractional DEs with p-Laplacian operator involving spatial singularity. The existence and uniqueness of solutions are derived with the help of the well-known Guo-Krasnoselskii theorem. Our work is a continuation of the study carried out in the recently published article " Chaos Solitons & Fractals. 2018;117:16-20." To manifest the results, we include an example with specific parameters and assumptions. (C) 2019 Elsevier Ltd. All rights reserved.
Citation - WoS: 49
Citation - Scopus: 84
Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law
(Mdpi, 2017) Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Guadalupe Lopez-Lopez, Maria; Manuel Alvarado-Martinez, Victor; Baleanu, Dumitru; Khan, Hasib; 56389; Matematik
In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.
Citation - WoS: 4
Citation - Scopus: 5
Derivation of dynamical integral inequalities based on two-dimensional time scales theory
(Springer, 2020) Khan, Zareen A.; Jarad, Fahd; Jarad, Fahd; Khan, Aziz; Khan, Hasib; 234808; Matematik
The main goal of this paper is to set up some new estimates of a specific class of dynamic integral inequalities (DII) which are partially linear on a time scale T with two independent variables. These, from the one hand, sum up and, on the other hand, offer a helpful method for both the qualitative and quantitative study of dynamic equations on time scales. Some applications are taken into consideration to show the validity of the fundamental results.
Citation - WoS: 63
Citation - Scopus: 72
Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system
(Pergamon-elsevier Science Ltd, 2020) Khan, Hasib; Jarad, Fahd; Khan, Aziz; Jarad, Fahd; Shah, Anwar; 234808; Matematik
The study of existence of solution ensures the essential conditions required for a solution. Keeping the importance of the study, we initiate the existence, uniqueness and data dependence of solutions an Atangana-Baleanu-Caputo (ABC)-fractional order differential impulsive system. For this purpose, the suggested ABC-fractional order differential impulsive system is transferred into equivalent fixed point problem via integral operator. The operator is then analyzed for boundedness, continuity and equicontinuity. Then Arzela-Ascolli theorem ensures the relatively compactness of the operator and the Schauder's fixed point theorem and Banach's fixed point theorem are utilized for the existence and uniqueness of solution. Data dependence and expressive application are also provided. (C) 2019 Elsevier Ltd. All rights reserved.
Citation - WoS: 43
Citation - Scopus: 50
Existence criterion for the solutions of fractional order p-Laplacian boundary value problems
(Springer, 2015) Jafari, Hossein; Baleanu, Dumitru; Baleanu, Dumitru; Khan, Hasib; Khan, Rahmat Ali; Khan, Aziz; Matematik
The existence criterion has been extensively studied for different classes in fractional differential equations (FDEs) through different mathematical methods. The class of fractional order boundary value problems (FOBVPs) with p-Laplacian operator is one of the most popular class of the FDEs which have been recently considered by many scientists as regards the existence and uniqueness. In this scientific work our focus is on the existence and uniqueness of the FOBVP with p-Laplacian operator of the form: D-gamma(phi(p)(D-theta z(t))) + a(t)f(z(t)) = 0, 3 < theta, gamma <= 4, t is an element of [0, 1], z(0) = z'''(0), eta D(alpha)z(t)vertical bar(t=1) = z'(0), xi z ''(1) - z ''(0) = 0, 0 < alpha < 1, phi(p)(D-theta z(t))vertical bar(t=0) = 0 = (phi(p)(D-theta z(t)))'vertical bar(t=0), (phi(p)(D-theta z(t)))''vertical bar(t=1) = 1/2(phi(p)(D-theta z(t)))''vertical bar(t=0), (phi(p)(D-theta z(t)))'''vertical bar(t=0) = 0, where 0 < xi, eta < 1 and D-theta, D-gamma, D-alpha are Caputo's fractional derivatives of orders theta, gamma, alpha, respectively. For this purpose, we apply Schauder's fixed point theorem and the results are checked by illustrative examples.
Citation - WoS: 81
Citation - Scopus: 86
Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application
(Amer inst Mathematical Sciences-aims, 2023) Alzabut, Jehad; Khan, Hasib; Alzabut, Jehad; Baleanu, Dumitru; Baleanu, Dumitru; Alobaidi, Ghada; Rehman, Mutti-Ur; 56389; Matematik
In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions; additionally, a numerical scheme based on the the Lagrange's interpolation polynomial is established and applied to a dynamical system for the applications. We also study the uniqueness and Hyers-Ulam stability for the solutions of the presumed mABC-FDEs system. Such a system has not been studied for the mentioned mABC-operator and this work generalizes most of the results studied for the ABC operator. This study will provide a base to a large number of dynamical problems for the existence, uniqueness and numerical simulations. The results are compared with the classical results graphically to check the accuracy and applicability of the scheme.
Citation - WoS: 14
Citation - Scopus: 14
Existence results for a general class of sequential hybrid fractional differential equations
(Springer, 2021) Khan, Rahmat Ali; Jarad, Fahd; Gul, Shaista; Jarad, Fahd; Khan, Hasib; 234808; Matematik
In this paper, we study a class of nonlinear boundary value problems (BVPs) consisting of a more general class of sequential hybrid fractional differential equations (SHFDEs) together with a class of nonlinear boundary conditions at both end points of the domain. The nonlinear functions involved depend explicitly on the fractional derivatives. We study the necessary conditions required for the unique solution to the suggested BVP under the Caratheodory conditions using the technique of measure of noncompactness and degree theory. We also develop conditions for uniqueness results and also on stability analysis.
Citation - WoS: 53
Citation - Scopus: 63
Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator
(Springer, 2017) Khan, Hasib; Baleanu, Dumitru; Li, Yongjin; Chen, Wen; Baleanu, Dumitru; Khan, Aziz; 56389; Matematik
In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo's sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is transferred to an integral system with the help of four Green functions G(alpha 1) (t, s), G(beta 1) (t, s), G(alpha 2) (t, s), G(beta 2) (t, s). Then using topological degree theory and Leray-Schauder's-type fixed point theorem, existence and uniqueness results are proved. An illustrative and expressive example is given as an application of the results.
Citation - WoS: 22
Citation - Scopus: 24
Inequalities for n-class of functions using the Saigo fractional integral operator
(Springer-verlag Italia Srl, 2019) Khan, Hasib; Baleanu, Dumitru; Tunc, Cemil; Baleanu, Dumitru; Khan, Aziz; Alkhazzan, Abdulwasea; 56389; Matematik
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.
Citation - WoS: 22
Citation - Scopus: 23
Modified Variational Iteration Method For Straight Fins With Temperature Dependent Thermal Conductivity
(Vinca inst Nuclear Sci, 2018) Inc, Mustafa; Baleanu, Dumitru; Khan, Hasib; Baleanu, Dumitru; Khan, Aziz; 56389; Matematik
The modified variational iteration method (MVIM) has been used to calculate the efficiency of straight fins with temperature dependent thermal conductivity. The obtained results are compared with homotopy analysis method (HAM), homotopy perturbation method (HPM), and Adomian decomposition method (ADM). It is used w # 0 auxiliary parameter to keep under control convergence region of solution series in MVIM. As a result, although MVIM and HAM give results close to each other; HPM and ADM give divergent results from analytical solution.
Citation - WoS: 14
Citation - Scopus: 13
New Method For Investigating the Density-Dependent Diffusion Nagumo Equation
(Vinca inst Nuclear Sci, 2018) Akgul, Ali; Baleanu, Dumitru; Hashemi, Mir Sajjad; Inc, Mustafa; Baleanu, Dumitru; Khan, Hasib; 56389; Matematik
We apply reproducing kernel method to the density-dependent diffusion Nagumo equation. Powerful method has been applied by reproducing kernel functions. The approximations to the exact solution are obtained. In particular, series solutions are obtained. These solutions demonstrate the certainty of the method The results acquired in this work conceive many attracted behaviors that assure further work on the Nagumo equation.
Citation - WoS: 5
Citation - Scopus: 6
Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications
(Springer, 2021) Khan, Zareen A.; Jarad, Fahd; Jarad, Fahd; Khan, Aziz; Khan, Hasib; 234808; Matematik
By means of sigma fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown functions. These inequalities are of a new form comparative with the current writing discoveries up until this point and can be viewed as a supportive strategy to assess the solutions of discrete partial differential equations numerically. We show a couple of employments of the compensated inequalities to reflect the benefits of our work. The main outcomes might be demonstrated by the use of the examination procedure and the approach of the mean value hypothesis.
Citation - WoS: 55
Citation - Scopus: 73
On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions
(Springer, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Khan, Hasib; Jafari, Hossein; Khan, Rahmat Ali; Alipour, Mohsen; Matematik
We investigate sufficient conditions for existence and uniqueness of solutions for a coupled system of fractional order hybrid differential equations (HDEs) with multi-point hybrid boundary conditions given by D-omega(x(t)/H(t, x(t), z(t))) = -K-1 (t, x(t), z(t)), omega epsilon (2, 3], D-epsilon(z(t)/G(t, x(t), z(t))) = -K-2 (t, x(t), z(t)), epsilon epsilon(2, 3] x(t)/H(t, x(t), z(t))vertical bar(t=1) = 0, D-mu(x(t)/H(t, x(t), z(t)))vertical bar(t=delta 1) =0, x((2))(0) = 0 z(t)/G(t, x(t), z(t))vertical bar(t=1) = 0, D-nu(z(t)/G(t, x(t), z(t)))vertical bar(t=delta 2) =0, z((2))(0) = 0 where t epsilon [0, 1], delta(1), delta(2), mu, upsilon epsilon (0, 1), and D-omega, D-epsilon, D-mu and D-upsilon are Caputo's fractional derivatives of order omega, is an element of, mu and nu, respectively, K-1, K-2 epsilon C([0, 1] x R x R, R) and G, H epsilon C([0, 1] x R x R, R - {0}). We use classical results due to Dhage and Banach's contraction principle (BCP) for the existence and uniqueness of solutions. For applications of our results, we include examples.
Citation - WoS: 5
Citation - Scopus: 5
On Iterative Solutions and Error Estimations of a Coupled System of Fractional Order Differential-Integral Equations with Initial and Boundary Conditions
(Springer india, 2020) Khan, Hasib; Baleanu, Dumitru; Jafari, Hossein; Baleanu, Dumitru; Khan, Rahmat Ali; Khan, Aziz; 56389; Matematik
The study of boundary value problems (BVPs) for fractional differential-integral equations (FDIEs) is extremely popular in the scientific community. Scientists are utilizing BVPs for FDIEs in day life problems by the help of different approaches. In this paper, we apply monotone iterative technique for the existence, uniqueness and the error estimations of solutions for a coupled system of BVPs for FDIEs of orders omega, epsilon. (3, 4]. The coupled system is given by D(omega)u (t) = -G(1) (t, I(omega)u (t), I(epsilon)v (t)), D-epsilon v (t) = -G(2) (t, I(omega)u (t), I-epsilon v (t)), D(delta)u (1) = 0 = I(3-omega)u (0) = I(4-omega)u (0), u(1) = Gamma(omega - d) /Gamma(omega) I omega-delta G(1)(t, I(omega)u (t), I(epsilon)v(t)) (t = 1), D(nu)v (1) = 0 = I3-epsilon v (0) = I4-nu v (0), v(1) = Gamma(epsilon - nu)/Gamma(epsilon) I epsilon-nu G(2)(t, I(omega)u (t), I-epsilon v (t)) (t = 1), where t is an element of [0, 1], delta, nu is an element of [1, 2]. The functions G(1), G(2) : [0, 1] x R x R. R, satisfy the Caratheodory conditions. The fractional derivatives D-omega, D-epsilon, D-delta, D-nu are in Riemann-Liouville sense and I-omega, I-epsilon, I3-omega, I4-epsilon, I3-epsilon, I4-epsilon, I omega-delta, I epsilon-nu are fractional order integrals. The assumed technique is a better approach for the existence, uniqueness and error estimation. The applications of the results are examined by the help of examples.
Citation - WoS: 30
Citation - Scopus: 30
On the exact solution of wave equations on cantor sets
(Mdpi, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Khan, Hasib; Jafari, Hossien; Khan, Rahmat Ali; Matematik
The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy. In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM). We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs). The efficiency of the scheme is examined by two illustrative examples.
Citation - WoS: 20
Citation - Scopus: 27
On the existence of solution for fractional differential equations of order 3 < delta(1) <= 4
(Springer, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Ravi P.; Khan, Hasib; Khan, Rahmat Ali; Jafari, Hossein; Matematik
In this paper, we deal with a fractional differential equation of order delta(1) is an element of (3,4] with initial and boundary conditions, D-delta 1 psi(x) = -H(x,psi(x)), D-alpha 1 psi(1) = 0 = I3-delta 1 psi(0) = I4-delta 1 psi(0), psi(1) = Gamma(delta(1)-alpha(1))/Gamma(nu(1)) I delta 1-alpha 1 H(x,psi(x))(1), where x is an element of [0, 1], alpha(1) is an element of (1, 2], addressing the existence of a positive solution (EPS), where the fractional derivatives D-delta 1, D-alpha 1 are in the Riemann-Liouville sense of the order delta(1), alpha(1), respectively. The function H is an element of C([0, 1] x R, R) and I delta 1-alpha 1 H(x, psi(x))(1) = 1/Gamma(delta(1)-alpha(1)) integral(1)(0) (1 -z)(delta 1-alpha 1-1) H(z,psi(z)) dz. To this aim, we establish an equivalent integral form of the problem with the help of a Green's function. We also investigate the properties of the Green's function in the paper which we utilize in our main result for the EPS of the problem. Results for the existence of solutions are obtained with the help of some classical results.
On the existence of solution for fractional differential equations of order 3< δ1≤4
(2015) Baleanu, Dumitru; Agarwal, Ravi P; Khan, Hasib; Khan, Rahmat Ali; Jafari, Hossein; 56389; Matematik
In this paper, we deal with a fractional differential equation of order δ1∈(3,4] with initial and boundary conditions, (Formula Presented), addressing the existence of a positive solution (EPS), where the fractional derivatives Dδ1, Dα1 are in the Riemann-Liouville sense of the order δ1, α1, respectively. The function (Formula Presented). To this aim, we establish an equivalent integral form of the problem with the help of a Green’s function. We also investigate the properties of the Green’s function in the paper which we utilize in our main result for the EPS of the problem. Results for the existence of solutions are obtained with the help of some classical results.
Citation - WoS: 33
Citation - Scopus: 42
Results for Mild solution of fractional coupled hybrid boundary value problems
(de Gruyter Poland Sp Z O O, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Jafari, Hossein; Khan, Hasib; Johnston, Sarah Jane; 56389; Matematik
The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray-Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.