Papers by Maysaa Alqurashi
Entropy, 2016
In this manuscript, we prove the existence and uniqueness of solutions for local fractional diffe... more In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some examples are presented to illustrate the validity of our results.
Journal of Nonlinear Sciences and Applications, 2016
We investigate new results about Lyapunov-type inequality by considering a fractional boundary va... more We investigate new results about Lyapunov-type inequality by considering a fractional boundary value problem subject to mixed boundary conditions. We give a necessary condition for nonexistence of solutions for a class of boundary value problems involving Riemann-Liouville fractional order. The order considered here is 3 < α ≤ 4. The investigation is based on a construction of Green's function and on finding its corresponding maximum value. In order to illustrate the result, we provide an application of Lyapunov-type inequality for an eigenvalue problem and we show how the necessary condition of existence can be employed to determine intervals for the real zeros of the Mittag-Leffler function.
Applications of Mathematics, 2004
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 49 (2004) APPLICATIONS OF MATHEMATICS No. 2, 141-164 NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS FOR SELFADJOINT DIFFERENTIAL EQUATIONS OF 2nth ORDER*
faculty.ksu.edu.sa
Page 1. Almansi functions near infinity in Rn M.Damlakhi, M.Al-Qurashi and V.Anandam Abstract: A ... more Page 1. Almansi functions near infinity in Rn M.Damlakhi, M.Al-Qurashi and V.Anandam Abstract: A characterization of continuous functions of the form u(x) = m Σ i=0 |x|i hi(x), where each hi(x) is a harmonic function defined outside a compact ...
SpringerPlus, 2016
Background Artificial neural networks (ANNs) are mathematical or computational models based on bi... more Background Artificial neural networks (ANNs) are mathematical or computational models based on biological neural networks. Neural networks consist of universal approximation potentiality, and they function best when the system has a high endurance to error when used to model. Recently, there have been rapid growth of ANNs which was utilized in various fields (
AIMS Mathematics
In this research, the Shehu transform is coupled with the Adomian decomposition method for obtain... more In this research, the Shehu transform is coupled with the Adomian decomposition method for obtaining the exact-approximate solution of the plasma fluid physical model, known as the Zakharov-Kuznetsov equation (briefly, ZKE) having a fractional order in the Caputo sense. The Laplace and Sumudu transforms have been refined into the Shehu transform. The action of weakly nonlinear ion acoustic waves in a plasma carrying cold ions and hot isothermal electrons is investigated in this study. Important fractional derivative notions are discussed in the context of Caputo. The Shehu decomposition method (SDM), a robust research methodology, is effectively implemented to generate the solution for the ZKEs. A series of Adomian components converge to the exact solution of the assigned task, demonstrating the solution of the suggested technique. Furthermore, the outcomes of this technique have generated important associations with the precise solutions to the problems being researched. Illustrati...
In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (X,N) by... more In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (X,N) by the help of integral-type contractions of self-quadruple mappings (SQMs), i.e., for ℘1,℘2,℘3,℘4 : X → R. For this, we assume that the SQMs are weakly compatible mappings and the pairs ( ℘1,℘3 ) and ( ℘2,℘4 ) satisfy the property (CLR℘3℘4). 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 ℘1,℘2,℘3,℘4, we do not need to the assumption of completeness of the MMS (X,N). 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.
This article aims to develop fractional order convolution theory to bring forth innovative method... more This article aims to develop fractional order convolution theory to bring forth innovative methods for generating fractional Fourier transforms by having recourse to solutions for fractional difference equations. It is evident that fractional difference operators are used to formulate for finding the solutions of problems of distinct physical phenomena. While executing the fractional Fourier transforms, a new technique describing the mechanism of interaction between fractional difference equations and fractional differential equations will be introduced as h tends to zero. Moreover, by employing the theory of discrete fractional Fourier transform of fractional calculus, the modeling techniques will be improved, which would help to construct advanced equipments based on fractional transforms technology using fractional Fourier decomposition method. Numerical examples with graphs are verified and generated by MATLAB.
By using the generalized beta function, we extend the fractional derivative operator of the Riema... more By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions. c ©2017 All rights reserved.
We investigate new results about Lyapunov-type inequality by considering a fractional boundary va... more We investigate new results about Lyapunov-type inequality by considering a fractional boundary value problem subject to mixed boundary conditions. We give a necessary condition for nonexistence of solutions for a class of boundary value problems involving Riemann–Liouville fractional order. The order considered here is 3 < α ≤ 4. The investigation is based on a construction of Green's function and on finding its corresponding maximum value. In order to illustrate the result, we provide an application of Lyapunov-type inequality for an eigenvalue problem and we show how the necessary condition of existence can be employed to determine intervals for the real zeros of the Mittag-Leffler function.
faculty.ksu.edu.sa
Page 1. Almansi functions near infinity in Rn M.Damlakhi, M.Al-Qurashi and V.Anandam Abstract: A ... more Page 1. Almansi functions near infinity in Rn M.Damlakhi, M.Al-Qurashi and V.Anandam Abstract: A characterization of continuous functions of the form u(x) = m Σ i=0 |x|i hi(x), where each hi(x) is a harmonic function defined outside a compact ...
Advances in Difference Equations
This article aims to develop fractional order convolution theory to bring forth innovative method... more This article aims to develop fractional order convolution theory to bring forth innovative methods for generating fractional Fourier transforms by having recourse to solutions for fractional difference equations. It is evident that fractional difference operators are used to formulate for finding the solutions of problems of distinct physical phenomena. While executing the fractional Fourier transforms, a new technique describing the mechanism of interaction between fractional difference equations and fractional differential equations will be introduced as h tends to zero. Moreover, by employing the theory of discrete fractional Fourier transform of fractional calculus, the modeling techniques will be improved, which would help to construct advanced equipments based on fractional transforms technology using fractional Fourier decomposition method. Numerical examples with graphs are verified and generated by MATLAB.
The Journal of Nonlinear Sciences and Applications
By using the generalized beta function, we extend the fractional derivative operator of the Riema... more By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions.
Asian-European Journal of Mathematics, 2011
The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multipl... more The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multiplication operators on the W *-algebra A is a unital GM-space, the base of the dual cone in the dual GL-space [Formula: see text] of which is affine isomorphic and weak*-homeomorphic to the state space of [Formula: see text]. It is shown that there exists a Lie *-isomorphism ϕ from the quotient (A ⊕∞ Aop)/K of an enveloping W *-algebra A ⊕∞ Aop of A by a weak*-closed Lie *-ideal K onto [Formula: see text], the restriction to the hermitian part ((A ⊕∞ Aop)/K)h of which is a bi-positive real linear isometry, thereby giving a characterization of the state space of [Formula: see text]. In the special case in which A is a W *-factor this leads to a further identification of the state space of [Formula: see text] in terms of the state space of A. For any W *-algebra A, the Banach-Lie *-algebra [Formula: see text] coincides with the set of generalized derivations of A, and, as an application, a f...
Asian-European J. …, 2011
The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multipl... more The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multiplication operators on the W *-algebra A is a unital GM-space, the base of the dual cone in the dual GL-space [Formula: see text] of which is affine isomorphic and weak*-homeomorphic to the state space of [Formula: see text]. It is shown that there exists a Lie *-isomorphism ϕ from the quotient (A ⊕∞ Aop)/K of an enveloping W *-algebra A ⊕∞ Aop of A by a weak*-closed Lie *-ideal K onto [Formula: see text], the restriction to the hermitian part ((A ⊕∞ Aop)/K)h of which is a bi-positive real linear isometry, thereby giving a characterization of the state space of [Formula: see text]. In the special case in which A is a W *-factor this leads to a further identification of the state space of [Formula: see text] in terms of the state space of A. For any W *-algebra A, the Banach-Lie *-algebra [Formula: see text] coincides with the set of generalized derivations of A, and, as an application, a formula is obtained for the norm of an element of [Formula: see text] in terms of a centre-valued &amp;amp;#39;norm&amp;amp;#39; on A, which is similar to that previously obtained by non-order-theoretic methods.
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Papers by Maysaa Alqurashi