Browsing by Author "Hussain, Amjad"

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Citation Count: Hussain, Amjad...et al. (2021). "Commutators of the Fractional Hardy Operator on Weighted Variable Herz-Morrey Spaces", Journal of Function Spaces, Vol. 2021.
Commutators of the Fractional Hardy Operator on Weighted Variable Herz-Morrey Spaces
(2021) Hussain, Amjad; Asim, Muhammad; Aslam, Muhammad; Jarad, Fahd; 234808
In the present paper, our aim is to establish the boundedness of commutators of the fractional Hardy operator and its adjoint operator on weighted Herz-Morrey spaces with variable exponents MKp,q⋅α⋅,λw.
Citation Count: Jhangeer, Adil...et al. (2020). "Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation", Results in Physics, Vol. 19.
Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation
(2020) Jhangeer, Adil; Hussain, Amjad; Junaid-U-Rehman, M.; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this paper, the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation is taken into consideration by means of Lie symmetry analysis. Infinitesimal generators are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Henceforth, conjugacy classes of abelian algebra are used to find the similarity reductions, which convert the considered equation into ordinary differential equations (ODEs). Further, these ODEs are taken into consideration, and travelling wave structures are computed by applying different techniques. Moreover, the discussed model is discussed by means of nonlinear selfadjointness and conservation laws are derived for each Lie symmetry generator. For specific values of the physical parameters of the equation under discussion, the graphical behaviour of some solutions is depicted. © 2020 The Authors
Citation Count: Hussain, Amjad...et al. (2020). "Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers-Huxley Equation", Symmetry-Basel, Vol. 12, No. 1.
Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers-Huxley Equation
(2020) Hussain, Amjad; Bano, Shahida; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this paper, we investigate a spatially two-dimensional Burgers-Huxley equation that depicts the interaction between convection effects, diffusion transport, reaction gadget, nerve proliferation in neurophysics, as well as motion in liquid crystals. We have used the Lie symmetry method to study the vector fields, optimal systems of first order, symmetry reductions, and exact solutions. Furthermore, using the power series method, a set of series solutions are obtained. Finally, conservation laws are derived using optimal systems.
Citation Count: Jhangeer, Adil...et al. (2021). "Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation", Chaos, Solitons and Fractals, Vol. 143.
Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation
(2021) Jhangeer, Adil; Hussain, Amjad; Junaid-U-Rehman, M.; Baleanu, Dumitru; Riaz, Muhammad Bilal; 56389
In this paper, the nonlinear modified Gardner (mG) equation is under consideration which represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron-positronion magneto plasmas. The considered model is investigated with the help of Lie group analysis. Lie point symmetries are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Furthermore, the one-dimensional optimal system of subalgebras is developed by adjoint technique and then we compute the similarity reductions corresponding to each vector field present in the optimal system, with the help of similarity reduction method we have to convert the PDE into the ODE. Some exact explicit solutions of obtained ordinary differential equations were constructed by the power series technique. With the aid of the Galilean transformation, the model is transformed into a planer dynamical system and the bifurcation behaviour is recorded. All practicable types of phase portraits with regard to the parameters of the problem considered are plotted. Meantime, sensitivity is observed by utilizing sensitivity analysis. In addition, the influence of physical parameters is studied by the application of an extrinsic periodic power. With additional perturbed term, quasi-periodic and quasi-periodic-chaotic behaviours is reported.
Citation Count: Hussain, Amjad; Asim, Muhammad; Jarad, Fahd (2022). "Variable λ-central morrey space estimates for the fractional hardy operators and commutators", Journal of Mathematics.
Variable λ-Central Morrey Space Estimates for the Fractional Hardy Operators and Commutators
(2022) Hussain, Amjad; Asim, Muhammad; Jarad, Fahd; 234808
Citation Count: Sarfraz, Naqash...et al. (2021). "Weighted Estimates for Commutator of Rough p -Adic Fractional Hardy Operator on Weighted p -Adic Herz-Morrey Spaces", Journal of Mathematics, Vol. 2021.
Weighted Estimates for Commutator of Rough p -Adic Fractional Hardy Operator on Weighted p -Adic Herz-Morrey Spaces
(2021) Sarfraz, Naqash; Filali, Doaa; Hussain, Amjad; Jarad, Fahd; 234808
The current article investigates the boundedness criteria for the commutator of rough p-adic fractional Hardy operator on weighted p-adic Lebesgue and Herz-type spaces with the symbol function from weighted p-adic bounded mean oscillations and weighted p-adic Lipschitz spaces.