Browsing by Author "Khan, Aziz"

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Citation Count: Khan, Aziz...et al. (2018). "A fixed point theorem on multiplicative metric space with integral-type inequality", Journal of Mathematics and Computer Science-Jmcs, Vol. 18, No. 1, pp. 18-28.
A fixed point theorem on multiplicative metric space with integral-type inequality
(Journal Mathematics & Computer Science-Jmcs, 2018) Khan, Aziz; Khan, Hasib; Baleanu, Dumitru; Jafari, Hossein; Khan, Tahir Saeed; Alqurashi, Maysaa; 56389
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 Count: Khan, Zareen A...et al. (2020). "Derivation of dynamical integral inequalities based on two-dimensional time scales theory", Journal of Inequalities and Applications, Vol. 2020, No. 1.
Derivation of dynamical integral inequalities based on two-dimensional time scales theory
(2020) Khan, Zareen A.; Jarad, Fahd; Khan, Aziz; Khan, Hasib; 234808
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 Count: Khan, Hasib...et al. (2020). "Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system", Chaos, Solitons and Fractals, Vol. 131.
Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system
(2020) Khan, Hasib; Khan, Aziz; Jarad, Fahd; Shah, Anwar; 234808
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. © 2019 Elsevier Ltd
Citation Count: Jafari, H...et al. (2015). Existence criterion for the solutions of fractional order p-Laplacian boundary value problems. Boundray Value Problems. http://dx.doi.org/ 10.1186/s13661-015-0425-2
Existence criterion for the solutions of fractional order p-Laplacian boundary value problems
(Springer International Publishing, 2015) Jafari, Hossein; Baleanu, Dumitru; Khan, Hasib; Khan, Rahmat Ali; Khan, Aziz
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 Count: Khan, Hasib...et al. (2017). Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator. Boundary Value Problems.
Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator
(Springer, 2017) Khan, Hasib; Li, Yongjin; Chen, Wen; Baleanu, Dumitru; Khan, Aziz; 56389
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 Count: Khan, Hasib...et al. (2019). "Inequalities for n-class of functions using the Saigo fractional integral operator", Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas, Vol. 113, No. 3, pp. 2407-2420.
Inequalities for n-class of functions using the Saigo fractional integral operator
(Springer Verlag Italia SRL, 2019) Khan, Hasib; Tunç, Cemil; Baleanu, Dumitru; Khan, Aziz; Alkhazzan, Abdulwasea; 56389
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 Count: Inc, Mustafa; Khan, Hasib; Baleanu, Dumitru; et al., "Modified Variational Iteration Method For Straight Fins With Temperature Dependent Thermal Conductivity", Thermal Science, Vol. 22, pp. S229-S236, (2018).
Modified Variational Iteration Method For Straight Fins With Temperature Dependent Thermal Conductivity
(Vinca Inst Nuclear Sci, 2018) İnç, Mustafa; Khan, Hasib; Baleanu, Dumitru; Khan, Aziz; 56389
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 Count: Khan, Zareen A...at all (2021). "Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications", Advances in Difference Equations, Vol. 2021, No. 1.
Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications
(2021) Khan, Zareen A.; Jarad, Fahd; Khan, Aziz; Khan, Hasib; 234808
By means of ς 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. © 2021, The Author(s).
Citation Count: Khan, Hasib...et al. (2020). "On Iterative Solutions and Error Estimations of a Coupled System of Fractional Order Differential-Integral Equations with Initial and Boundary Conditions", Differential Equations and Dynamical Systems, Vol. 28, no. 4, pp. 1059-1071.
On Iterative Solutions and Error Estimations of a Coupled System of Fractional Order Differential-Integral Equations with Initial and Boundary Conditions
(2020) Khan, Hasib; Jafari, Hossein; Baleanu, Dumitru; Khan, Rahmat Ali; Khan, Aziz; 56389
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 ω, ϵ∈ (3 , 4]. The coupled system is given by Dωu(t)=-G1(t,Iωu(t),Iεv(t)),Dεv(t)=-G2(t,Iωu(t),Iεv(t)),Dδu(1)=0=I3-ωu(0)=I4-ωu(0),u(1)=Γ(ω-δ)Γ(ω)Iω-δG1(t,Iωu(t),Iεv(t))(t=1),Dνv(1)=0=I3-εv(0)=I4-νv(0),v(1)=Γ(ε-ν)Γ(ε)Iε-νG2(t,Iωu(t),Iεv(t))(t=1),where t∈ [0 , 1] , δ, ν∈ [1 , 2]. The functions G1, G2: [0 , 1] × R× R→ R, satisfy the Caratheodory conditions. The fractional derivatives Dω, Dε, Dδ, Dν are in Riemann-Liouville sense and Iω, Iε, I3-ω, I4-ω, I3-ε, I4-ε, Iω-δ, Iε-ν 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. © 2017, Foundation for Scientific Research and Technological Innovation.
Citation Count: Devi, Amita...et al. (20209. "On stability analysis and existence of positive solutions for a general non-linear fractional differential equations", Advances in Difference Equations, Vol. 2020, No. 1.
On stability analysis and existence of positive solutions for a general non-linear fractional differential equations
(2020) Devi, Amita; Kumar, Anoop; Baleanu, Dumitru; Khan, Aziz; 56389
In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Laplacian operator. Also we investigate the Hyers-Ulam (HU) stability of solutions. For the existence result, we establish the integral form of the FDE by using the Green function and then the existence of a solution is obtained by applying Guo-Krasnoselskii's fixed point theorem. For our purpose, we also check the properties of the Green function. The uniqueness of the result is established by applying the Banach contraction mapping principle. An example is offered to ensure the validity of our results.