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Mohammed K. A. Kaabar

Bio: Mohammed K. A. Kaabar is an academic researcher from University of Malaya. The author has contributed to research in topics: Boundary value problem & Fractional calculus. The author has an hindex of 5, co-authored 34 publications receiving 83 citations. Previous affiliations of Mohammed K. A. Kaabar include United Nations & Washington State University.

Papers
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TL;DR: In this paper, a generalized fractional derivative (GFD) definition is proposed for a differentiable function expanded by a Taylor series, and GFD is applied for some functions to investigate that the GFD coincides with the results from Caputo and Riemann–Liouville fractional derivatives.
Abstract: A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function expanded by a Taylor series, we show that . GFD is applied for some functions to investigate that the GFD coincides with the results from Caputo and Riemann–Liouville fractional derivatives. The solutions of the Riccati fractional differential equation are obtained via the GFD. A comparison with the Bernstein polynomial method , enhanced homotopy perturbation method , and conformable derivative is also discussed. Our results show that the proposed definition gives a much better accuracy than the well-known definition of the conformable derivative. Therefore, GFD has advantages in comparison with other related definitions. This work provides a new path for a simple tool for obtaining analytical solutions of many problems in the context of fractional calculus.

70 citations

Journal ArticleDOI
TL;DR: Deep learning (DL) is a branch of machine learning and artificial intelligence that has been applied to many areas in different domains such as health care and drug design as mentioned in this paper, which has emerged as a technology of choice due to the availability of high computational resources.
Abstract: Deep learning (DL) is a branch of machine learning and artificial intelligence that has been applied to many areas in different domains such as health care and drug design. Cancer prognosis estimates the ultimate fate of a cancer subject and provides survival estimation of the subjects. An accurate and timely diagnostic and prognostic decision will greatly benefit cancer subjects. DL has emerged as a technology of choice due to the availability of high computational resources. The main components in a standard computer-aided design (CAD) system are preprocessing, feature recognition, extraction and selection, categorization, and performance assessment. Reduction of costs associated with sequencing systems offers a myriad of opportunities for building precise models for cancer diagnosis and prognosis prediction. In this survey, we provided a summary of current works where DL has helped to determine the best models for the cancer diagnosis and prognosis prediction tasks. DL is a generic model requiring minimal data manipulations and achieves better results while working with enormous volumes of data. Aims are to scrutinize the influence of DL systems using histopathology images, present a summary of state-of-the-art DL methods, and give directions to future researchers to refine the existing methods.

41 citations

Journal ArticleDOI
TL;DR: In this paper, a novel analytical method for solving nonlinear partial differential equations is studied, known as triple Laplace transform decomposition method, which is generalized in the sense of conformable derivative.
Abstract: In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.

24 citations

Journal ArticleDOI
29 Jul 2021
TL;DR: In this paper, the existence of extremal solutions for a class of ψ-Caputo fractional differential equations with nonlinear boundary conditions was proved using monotone iterative technique together with the method of upper and lower solutions.
Abstract: The main contribution of this paper is to prove the existence of extremal solutions for a novel class of ψ-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of upper and lower solutions. Finally, we provide an example along with graphical representations to confirm the validity of our main results.

24 citations


Cited by
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[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Book ChapterDOI
01 Jan 2015

3,828 citations

Book
01 Jan 1982
TL;DR: Theorem of Borsuk and Topological Transversality as mentioned in this paper, the Lefschetz-Hopf Theory, and fixed point index are the fundamental fixed point theorem.
Abstract: Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index

688 citations

Dissertation
01 Mar 2009
TL;DR: In this paper, the relationship between these transforms and their properties was discussed and some important applications in physics and engineering were given, as well as their properties and applications in various domains.
Abstract: Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

383 citations