Author

# Fatemah Mofarreh

Other affiliations: University of Wollongong

Bio: Fatemah Mofarreh is an academic researcher from Princess Nora bint Abdul Rahman University. The author has contributed to research in topics: Mathematics & Submanifold. The author has an hindex of 4, co-authored 31 publications receiving 67 citations. Previous affiliations of Fatemah Mofarreh include University of Wollongong.

##### Papers

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TL;DR: In this article, the Adomian decomposition method is used to solve fractional-order parabolic equations using an innovative analytical technique, which is well supported by natural transform to establish closed form solutions for targeted problems.

Abstract: This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.

30 citations

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TL;DR: In this paper, it was shown that if the Laplacian and gradient of the warping function of a compact warped product submanifold in the hyperbolic space satisfy various extrinsic restrictions, then has no stable integral currents, and its homology groups are trivial.

Abstract: In this paper, we show that if the Laplacian and gradient of the warping function of a compact warped product submanifold in the hyperbolic space satisfy various extrinsic restrictions, then has no stable integral currents, and its homology groups are trivial. Also, we prove that the fundamental group is trivial. The restrictions are also extended to the eigenvalues of the warped function, the integral Ricci curvature, and the Hessian tensor. The results obtained in the present paper can be considered as generalizations of the Fu–Xu theorem in the framework of the compact warped product submanifold which has the minimal base manifold in the corresponding ambient manifolds.

21 citations

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TL;DR: In this paper, the authors studied the asymptotic behavior of fourth-order advanced differential equations of the form aυw′′υβ′+qυgwδυ=0.

Abstract: We studied the asymptotic behavior of fourth-order advanced differential equations of the form aυw′′′υβ′+qυgwδυ=0. New results are presented for the oscillatory behavior of these equations in the form of Philos-type and Hille–Nehari oscillation criteria. Some illustrative examples are presented.

21 citations

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TL;DR: In this paper , the authors focused on time-like circular surfaces and singularities in Minkowski 3-space and determined a different kind of timelike circular surface was determined and named the time-ike roller coaster surface, which can be swept out by moving a Lorentzian circle with its center while following a nonlightlike curve called the spine curve.

Abstract: The present paper is focused on time-like circular surfaces and singularities in Minkowski 3-space. The timelike circular surface with a constant radius could be swept out by moving a Lorentzian circle with its center while following a non-lightlike curve called the spine curve. In the present study, we have parameterized timelike circular surfaces and examined their geometric properties, such as singularities and striction curves, corresponding with those of ruled surfaces. After that, a different kind of timelike circular surface was determined and named the timelike roller coaster surface. Meanwhile, we support the results of this work with some examples.

19 citations

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TL;DR: In this paper, it was shown that closed, convex, axially symmetric hypersurfaces contract under the flow to round points, and hypersurface contracting self-similarly are necessarily spheres.

Abstract: Recently, fully nonlinear curvature flow of a certain class of axially symmetric hypersurfaces with boundary conditions time of existence was obtained, in the case of convex speeds (J. A. McCoy et al., Annali di Matematica Pura ed Applicata 1–13, 2013). In this paper we remove the convexity condition on the speed in the case it is homogeneous of degree one in the principal curvatures and the boundary conditions are pure Neumann. Moreover, we classify the singularities of the flow of a larger class of axially symmetric hypersurfaces as Type I. Our approach to remove the convexity requirement on the speed is based upon earlier work of Andrews for evolving convex surfaces (B. H. Andrews, Invent Math 138(1):151–161, 1999; Calc Var Partial Differ Equ 39(3–4):649–657, 2010); these arguments for obtaining a ‘curvature pinching estimate’ may be adapted to this setting due to axial symmetry. As further applications of curvature pinching in this setting, we show that closed, convex, axially symmetric hypersurfaces contract under the flow to round points, and hypersurfaces contracting self-similarly are necessarily spheres. These results are new for n ≥ 3.

18 citations

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511 citations

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477 citations

01 Jan 2016

TL;DR: In this article, the authors present a broad overview of the application of the Hopf maximum principle in the study of partial differential equations (PDE) with a focus on elliptic and hyperbolic solutions.

Abstract: This book is devoted to the study of maximum principles in partial differential equations. I t contains a wealth of material much of which is presented for the first time in a book form. An attractive feature of the book is that it is completely elementary and thus accessible to a wide audience of readers. The book has four chapters. Chapter I deals with the one dimensional maximum principle. The discussion of this very simple model of a maximum principle forms a good introduction to the general theory. Various applications of the principle are given to show that it is a very useful tool even in the study of ordinary differential equations. As an example, it is shown that many oscillation and comparison results in the Sturm-Liouville theory could be deduced most easily by a maximum principle argument. The proper discussion of maximum principles in partial differential equations begins in Chapter II . This chapter, which is the backbone of the book, is devoted to elliptic equations. The material covered in this chapter includes the E. Hopf maximum principle and its generalizations; the Phragmèn-Lindelöf principle for solutions of elliptic equations; Serrin's version of the Harnack inequality for solutions of general elliptic equations in two variables (this is probably the most difficult result discussed in the book) ; various versions of the Hadamard three circles theorems for solutions of elliptic equations; applications of the maximum principle to nonlinear equations and to problems of fluid flow. Chapter III is devoted to parabolic equations. The plan of this chapter parallels that of Chapter II . The topics discussed include the L. Nirenberg strong maximum principle; a three curves theorem with an interesting application to the Tikhonov uniqueness theorem; a Phragmèn-Lindelöf principle for parabolic equations with applications to uniqueness results; nonlinear operators; a maximum principle for certain parabolic systems. The fourth and the last chapter is devoted to hyperbolic equations. The results in this chapter are somewhat special since a maximum principle in the proper sense does not hold for solutions of hyperbolic equations. Nevertheless, solutions of certain hyperbolic equations

207 citations

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TL;DR: In this article , the homotopy perturbation transform (HPT) was applied to analyze fractional-order nonlinear fifth-order Korteweg-de-Vries-type (KdV-type)/Kawahara-type equations.

Abstract: This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. This method combines the Zain Ul Abadin Zafar-transform (ZZ-T) and the homotopy perturbation technique (HPT) to show the validation and efficiency of this technique to investigate three examples. It is also shown that the fractional and integer-order solutions have closed contact with the exact result. The suggested technique is found to be reliable, efficient, and straightforward to use for many related models of engineering and several branches of science, such as modeling nonlinear waves in different plasma models.

44 citations