Browsing by Author "Ibrahim, Rabha W."

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Citation - WoS: 13
Citation - Scopus: 19
A New Medical Image Enhancement Algorithm Based on Fractional Calculus
(Tech Science Press, 2021) Jalab, Hamid A.; Baleanu, Dumitru; Ibrahim, Rabha W.; Hasan, Ali M.; Karim, Faten Khalid; Al-Shamasneh, Ala'a R.; Baleanu, Dumitru; 56389; Matematik
The enhancement of medical images is a challenging research task due to the unforeseeable variation in the quality of the captured images. The captured images may present with low contrast and low visibility, which might influence the accuracy of the diagnosis process. To overcome this problem, this paper presents a new fractional integral entropy (FITE) that estimates the unforeseeable probabilities of image pixels, posing as the main contribution of the paper. The proposed model dynamically enhances the image based on the image contents. The main advantage of FITE lies in its capability to enhance the low contrast intensities through pixels? probability. Initially, the pixel probability of the fractional power is utilized to extract the illumination value from the pixels of the image. Next, the contrast of the image is then adjusted to enhance the regions with low visibility. Finally, the fractional integral entropy approach is implemented to enhance the low visibility contents from the input image. Tests were conducted on brain MRI, lungs CT, and kidney MRI scans datasets of different image qualities to show that the proposed model is robust and can withstand dramatic variations in quality. The obtained comparative results show that the proposed image enhancement model achieves the best BRISQUE and NIQE scores. Overall, this model improves the details of brain MRI, lungs CT, and kidney MRI scans, and could therefore potentially help the medical staff during the diagnosis process.
Citation - WoS: 11
Citation - Scopus: 13
Analytic Solution of the Langevin Differential Equations Dominated by a Multibrot Fractal Set
(Mdpi, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
We present an analytic solvability of a class of Langevin differential equations (LDEs) in the asset of geometric function theory. The analytic solutions of the LDEs are presented by utilizing a special kind of fractal function in a complex domain, linked with the subordination theory. The fractal functions are suggested for the multi-parametric coefficients type motorboat fractal set. We obtain different formulas of fractal analytic solutions of LDEs. Moreover, we determine the maximum value of the fractal coefficients to obtain the optimal solution. Through the subordination inequality, we determined the upper boundary determination of a class of fractal functions holding multibrot function v(z)=1+3 kappa z+z(3).
Citation - WoS: 2
Citation - Scopus: 4
Analytic Studies of a Class of Langevin Differential Equations Dominated by a Class of Julia Fractal Functions
(Univ Kragujevac, Fac Science, 2024) Baleanu, Dumitru; Baleanu, Dumitru; Matematik
. In this investigation, we study a class of analytic functions of type Carath & eacute;o dory style in the open unit disk connected with some fractal domains. This class of analytic functions is formulated based on a kind of Langevin differential equations (LDEs). We aim to study the analytic solvability of LDEs in the advantage of geometric function theory consuming the geometric properties of the Julia fractal (JF) and other fractal connected with the logarithmic function. The analytic solutions of the LDEs are obtainable by employing the subordination theory.
Citation - WoS: 2
Citation - Scopus: 3
Conformable differential operators for meromorphically multivalent functions
(de Gruyter Poland Sp Z O O, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; Jahangiri, Jay M.; 56389; Matematik
We define a conformable diff-integral operator for a class of meromorphically multivalent functions. We show that this conformable operator adheres to the semigroup property. We then use the subordination properties to prove inclusion conditions, sufficienrt inclusion conditions and convolution properties for this class of conformable operators.
Citation - WoS: 5
Citation - Scopus: 6
Convoluted fractional differentials of various forms utilizing the generalized Raina's function description with applications
(Taylor & Francis Ltd, 2022) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equations involving the suggested operator is studied. As seen, the solution is provided by a certain hypergeometric function. We also create a fractional coefficient differential operator. Its geometric and analytic features are discussed. Finally, we use the Jackson's calculus to expand the Raina's differential operator and investigate its properties in relation to geometric function theory.
Citation - WoS: 1
Citation - Scopus: 2
Entire solutions of a class of algebraic Briot-Bouquet differential equations utilizing majority concept
(Springer, 2020) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this effort, the analytic solution of a class of algebraic Briot-Bouquet differential equations (ABBDE) in the open unit disk is investigated by making use of a major theory. The class is presented by the formula alpha(1)phi ' 3(z)+alpha(2)phi'(z)phi(z)+alpha(3)phi '(z)phi(2)(z)+aleph(k)(phi)(z)=0, aleph(k)(phi)(z):=a(k)phi(k)(z)+a(k-1)phi(k-1)(z)+...+a(1) phi(z)+a(0). The conformal analysis (angle-preserving) of the ABBDEs is considered. Analytic outcomes of the ABBDEs are indicated by employing the major method. Some special cases are investigated.
Citation - WoS: 1
Citation - Scopus: 1
Fractional Heat Equation Optimized By A Chaotic Function
(Vinca inst Nuclear Sci, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Wazi, Mayada T.; Baleanu, Dumitru; Al-Saidi, Nadia; 56389; Matematik
In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.
Citation - WoS: 10
Citation - Scopus: 9
Fractional Rényi Entropy Image Enhancement for Deep Segmentation of Kidney MRI
(Tech Science Press, 2021) Jalab, Hamid A.; Baleanu, Dumitru; Al-Shamasneh, Ala'a R.; Shaiba, Hadil; Ibrahim, Rabha W.; Baleanu, Dumitru; 56389; Matematik
Recently, many rapid developments in digital medical imaging have made further contributions to health care systems. The segmentation of regions of interest in medical images plays a vital role in assisting doctors with their medical diagnoses. Many factors like image contrast and quality affect the result of image segmentation. Due to that, image contrast remains a challenging problem for image segmentation. This study presents a new image enhancement model based on fractional Renyi entropy for the segmentation of kidney MRI scans. The proposed work consists of two stages: enhancement by fractional Renyi entropy, and MRI Kidney deep segmentation. The proposed enhancement model exploits the pixel's probability representations for image enhancement. Since fractional Renyi entropy involves fractional calculus that has the ability to model the non-linear complexity problem to preserve the spatial relationship between pixels, yielding an overall better details of the kidney MRI scans. In the second stage, the deep learning kidney segmentation model is designed to segment kidney regions in MRI scans. The experimental results showed an average of 95.60% dice similarity index coefficient, which indicates best overlap between the segmented bodies with the ground truth. It is therefore concluded that the proposed enhancement model is suitable and effective for improving the kidney segmentation performance.
Citation - WoS: 0
Citation - Scopus: 1
Generalized Quantum Integro-Differential Fractional Operator with Application of 2D-Shallow Water Equation in a Complex Domain
(Mdpi, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic functions, we present a set of integral inequalities using the concepts of subordination and superordination. In addition, as an application, we determine the maximum and minimum solutions of the extended fractional 2D-shallow water equation in a complex domain.
Citation - WoS: 6
Citation - Scopus: 6
Geometric behavior of a class of algebraic differential equations in a complex domain using a majorization concept
(Amer inst Mathematical Sciences-aims, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by alpha[phi(z)phi ''(z) + (phi'(z))(2)] + a(m)phi(m)(z) + a(m-1)phi(m-1)(z) + ... + a(1)phi(z) + a(0) = 0. The conformal analysis (angle-preserving) of the CADEs is investigated. We present sufficient conditions to obtain analytic solutions of the CADEs. We show that these solutions are subordinated to analytic convex functions in terms of e(z). Moreover, we investigate the connection estimates (coefficient bounds) of CADEs by employing the majorization method. We achieve that the coefficients bound are optimized by Bernoulli numbers.
Citation - WoS: 7
Citation - Scopus: 7
Global stability of local fractional Hénon-Lozi map using fixed point theory
(Amer inst Mathematical Sciences-aims, 2022) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
We present an innovative piecewise smooth mapping of the plane as a parametric discrete-time chaotic system that has robust chaos over a share of its significant organization parameters and includes the generalized Henon and Lozi schemes as two excesses and other arrangements as an evolution in between. To obtain the fractal Henon and Lozi system, the generalized Henon and Lozi system is defined by adopting the fractal idea (FHLS). The recommended system's dynamical performances are investigated from many angles, such as global stability in terms of the set of fixed points.
Citation - WoS: 8
Citation - Scopus: 9
Image Encryption Algorithm Based on New Fractional Beta Chaotic Maps
(Tech Science Press, 2022) Ibrahim, Rabha W.; Baleanu, Dumitru; Natiq, Hayder; Alkhayyat, Ahmed; Farhan, Alaa Kadhim; Al-Saidi, Nadia M. G.; Baleanu, Dumitru; 56389; Matematik
In this study, a new algorithm of fractional beta chaotic maps is proposed to generate chaotic sequences for image encryption. The proposed technique generates multi random sequences by shuffling the image pixel position. This technique is used to blur the pixels connecting the input and encrypted images and to increase the attack resistance. The proposed algorithm makes the encryption process sophisticated by using fractional chaotic maps, which hold the properties of pseudo-randomness. The fractional beta sequences are utilized to alter the image pixels to decryption attacks. The experimental results proved that the proposed image encryption algorithm successfully encrypted and decrypted the images with the same keys. The output findings indicate that our proposed algorithm has good entropy and low correlation coefficients. This translates to enhanced security against different attacks. A MATLAB programming tool was used to implement and assess the image quality measures. A comparison with other image encryption techniques regarding the visual inspection and signal-to-noise ratio is provided.
Citation - WoS: 4
Citation - Scopus: 9
Image Splicing Detection Based on Texture Features with Fractal Entropy
(Tech Science Press, 2021) Al-Azawi, Razi J.; Baleanu, Dumitru; Al-Saidi, Nadia M. G.; Jalab, Hamid A.; Ibrahim, Rabha W.; Baleanu, Dumitru; 56389; Matematik
Over the past years, image manipulation tools have become widely accessible and easier to use, which made the issue of image tampering far more severe. As a direct result to the development of sophisticated image-editing applications, it has become near impossible to recognize tampered images with naked eyes. Thus, to overcome this issue, computer techniques and algorithms have been developed to help with the identification of tampered images. Research on detection of tampered images still carries great challenges. In the present study, we particularly focus on image splicing forgery, a type of manipulation where a region of an image is transposed onto another image. The proposed study consists of four features extraction stages used to extract the important features from suspicious images, namely, Fractal Entropy (FrEp), local binary patterns (LBP), Skewness, and Kurtosis. The main advantage of FrEp is the ability to extract the texture information contained in the input image. Finally, the "support vector machine" (SVM) classification is used to classify images into either spliced or authentic. Comparative analysis shows that the proposed algorithm performs better than recent state-of-the-art of splicing detection methods. Overall, the proposed algorithm achieves an ideal balance between performance, accuracy, and efficacy, which makes it suitable for real-world applications.
Citation - WoS: 0
Citation - Scopus: 2
Image Splicing Detection Using Generalized Whittaker Function Descriptor
(Tech Science Press, 2023) Baleanu, Dumitru; Baleanu, Dumitru; Al-Shamayleh, Ahmad Sami; Ibrahim, Rabha W.; 56389; Matematik
Image forgery is a crucial part of the transmission of misinfor-mation, which may be illegal in some jurisdictions. The powerful image editing software has made it nearly impossible to detect altered images with the naked eye. Images must be protected against attempts to manipulate them. Image authentication methods have gained popularity because of their use in multimedia and multimedia networking applications. Attempts were made to address the consequences of image forgeries by creating algorithms for identifying altered images. Because image tampering detection targets processing techniques such as object removal or addition, identifying altered images remains a major challenge in research. In this study, a novel image texture feature extraction model based on the generalized k-symbol Whittaker function (GKSWF) is proposed for better image forgery detection. The proposed method is divided into two stages. The first stage involves feature extraction using the proposed GKSWF model, followed by classification using the "support vector machine" (SVM) to distinguish between authentic and manipulated images. Each extracted feature from an input image is saved in the features database for use in image splicing detection. The proposed GKSWF as a feature extraction model is intended to extract clues of tam-pering texture details based on the probability of image pixel. When tested on publicly available image dataset "CASIA" v2.0 (Chinese Academy of Sciences, Institute of Automation), the proposed model had a 98.60% accuracy rate on the YCbCr (luminance (Y), chroma blue (Cb) and chroma red (Cr)) color spaces in image block size of 8 x 8 pixels. The proposed image authentication model shows great accuracy with a relatively modest dimension feature size, supporting the benefit of utilizing the k-symbol Whittaker function in image authentication algorithms.
Citation - WoS: 5
Citation - Scopus: 7
Mathematical design enhancing medical images formulated by a fractal flame operator
(Tech Science Press, 2022) Ibrahim, Rabha W.; Baleanu, Dumitru; Yahya, Husam; Mohammed, Arkan J.; Al-Saidi, Nadia M. G.; Baleanu, Dumitru; 56389; Matematik
The interest in using fractal theory and its applications has grown in the field of image processing. Image enhancement is one of the feature processing tools, which aims to improve the details of an image. The enhancement of digital pictures is a challenging task due to the unforeseeable variation in the quality of the captured images. In this study, we present a mathematical model using a local conformable differential operator (LCDO). The proposed model is formulated by the theory of cantor fractal to generalize the definition of LCDO. The main advantage of utilizing LCDO for image enhancement is its capability to enhance the low contrast intensities using the coefficient estimate of LCDO. The proposed image enhancement algorithm is tested against different images with different qualities to show that it is robust and can withstand dramatic variations in quality. The quantitative results of Brisque, and Piqe were 30.38 and 35.53 respectively. The comparative consequences indicate that the proposed image enhancement model realizes the best image quality assessments. Overall, this model significantly improves the details of the given datasets, and can potentially help the medical staff during the diagnosis process. A MATLAB programming instrument utilized for application and valuation of the image quality measures. A comparison with other image techniques is illustrated regarding the visual review.
Citation - WoS: 3
Citation - Scopus: 2
Modified Atangana-Baleanu Fractional Differential Operators
(inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2022) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
Fractional differential operators are mostly investigated for functions of real variables. In this paper, we present two fractional differential operators for a class of normalized analytic functions in the open unit disk. The suggested operators are investigated according to concepts in geometric function theory, using the concepts of convexity and starlikeness. Therefore, we reformulate the new operators in the Ma-Minda class of analytic functions, in order to act on normalized analytic functions. Our method is based on subordination, superordination, and majorization theory. As an application, we employ these operators to generalize Bernoulli's equation and a special class of Briot-Bouquet equations. The solution of the generalized equation is formulated by a hypergeometric function.
Citation - WoS: 7
Citation - Scopus: 10
On a combination of fractional differential and integral operators associated with a class of normalized functions
(Amer inst Mathematical Sciences-aims, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
Recently, the combined fractional operator (CFO) is introduced and discussed in Baleanu et al. [1] in real domain. In this paper, we extend CFO to the complex domain and study its geometric properties in some normalized analytic functions including the starlike and convex functions. Moreover, we employ the complex CFO to modify a class of Briot-Bouquet differential equations in a complex region. As a consequence, the upper solution is illustrated by using the concept of subordination inequality.
Citation - WoS: 0
Citation - Scopus: 0
On a geometric study of a class of normalized functions defined by Bernoulli’s formula
(Springer, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Aldawish, Ibtisam; Baleanu, Dumitru; 56389; Matematik
The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli's formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class.
Citation - WoS: 1
Citation - Scopus: 3
On a new linear operator formulated by Airy functions in the open unit disk
(Springer, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk.
Citation - WoS: 30
Citation - Scopus: 34
On quantum hybrid fractional conformable differential and integral operators in a complex domain
(Springer-verlag Italia Srl, 2021) Ibrahim, Rabha W.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
Newly, the hybrid fractional differential operator (HFDO) is presented and studied in Baleanu et al. (Mathematics 8.3:360, 2020). This work deals with the extension of HFDO to the complex domain and its generalization by using the quantum calculus. The outcome of the above conclusion is a q-HFDO, which will employ to introduce some classes of normalized analytic functions containing the well-known starlike and convex classes. Moreover, we utilize the quantum calculus to formulate the q-integral operator corresponding to q-HFDO. As a result, the upper solution is exemplified by utilizing the notion of subordination inequality.