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Article
Physics, Applied
Safoura Rezaei Aderyani et al.
Summary: In this study, various analytical techniques were applied to obtain approximate and analytic solutions of several nonlinear partial differential equations. The numerical results were presented in tables and the advantages and disadvantages of the mentioned methods were discussed, resulting in conclusions.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Engineering, Electrical & Electronic
Sandeep Malik et al.
Summary: The purpose of this work is to find innovative exact solutions for nonlinear partial differential equations using the new Kudryashov approach. The technique provides novel exact solutions of soliton types. 3D and 2D plots of higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are shown to better understand the nonlinear wave structures. The new Kudryashov technique is effective and simple, providing new generalized solitonic wave profiles that enhance the understanding of the development and dynamic nature of such models.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Mathematics
Safoura Rezaei Aderyani et al.
Summary: The aim of this study is to obtain different analytical solutions to the space-time fractional Bogoyavlenskii equation and the conformable time-fractional-modified nonlinear Schrodinger equation, which describe the fluctuation of sea waves and the propagation of water waves in ocean engineering. The G'/G(2) -expansion method is applied to investigate the dynamics of solitons and the existence of solutions. The accomplished solutions are useful for wave fluctuation description, wave propagation survey, and experimental and numerical verification in ocean engineering.
Article
Computer Science, Artificial Intelligence
Xindong Si et al.
Summary: This paper focuses on achieving finite-time synchronization of delayed fractional-order memristive neural networks (FMNNs) using quantized control. Two types of quantized controllers are designed to eliminate residual synchronization errors caused by memristive connection weights. By combining the direct estimation method with the Gronwall inequality technique, drive-response FMNNs with dependency-based FTS criteria are derived. The advantages of the derived synchronization criteria are discussed in terms of theory and simulation, and the relationship between the finite-time parameter and quantization parameters is displayed. Two examples are provided to demonstrate the effectiveness of the obtained results.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: In this paper, new control functions are defined using special functions, introducing the concept of multi-stability. The multi-stability of homomorphisms in C*-algebras and Lie C*-algebras, as well as the multi-stability of derivations in C*-algebras, are investigated. The random operator equation is analyzed using fixed point methods, with a particular focus on Jensen's random operator equation when mu=1.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2023)
Article
Mathematics
Safoura Rezaei Aderyani et al.
Summary: We use Mittag-Leffler-type functions to introduce a class of matrix-valued fuzzy controllers, which enable us to propose the concept of multi-stability and obtain fuzzy approximate solutions of matrix-valued fractional differential equations in fuzzy spaces. The concept of multi-stability allows us to obtain different approximations depending on the initially chosen special functions. Additionally, we investigate the Ulam-Hyers stability of the models by utilizing various properties of a function of Mittag-Leffler type.
Article
Mathematics, Interdisciplinary Applications
Omar Kahouli et al.
Summary: The goal of this work is to prove the existence and uniqueness of solutions to a class of Hadamard Fractional Ito-Doob Stochastic integral equations (HFIDSIE) of order phi ∈ (0, 1) using the fixed point technique (FPT). Hyers-Ulam stability (HUS) for HFIDSIE is studied using the Gronwall inequality. Two theoretical examples are provided to illustrate the results.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Multidisciplinary Sciences
Naveed Khan et al.
Summary: In this paper, the dynamics of a chaotic system based on a circuit design is analyzed using the newly developed Fractal-Fractional derivative with power law kernel. The problem is modeled using classical order nonlinear, coupled ordinary differential equations, which are then generalized through Fractal-Fractional derivative with power law kernel. The theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. A numerical technique using MATLAB software is used to analyze the highly non-linear fractal-fractional order system. The graphical solutions are presented in two dimensional graphs and three dimensional phase portraits and discussed in detail, with some concluding remarks drawn from the study. It is worth noting that fractal-fractional differential operators can quickly converge the dynamics of a chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.
SCIENTIFIC REPORTS
(2023)
Article
Materials Science, Multidisciplinary
Phil Krabbe et al.
Summary: We study increasing subsequences (ISs) in an ensemble of sequences generated by a permutation of numbers {1, 2, ..., n}. By considering a Boltzmann ensemble at temperature T, we are able to analyze the equilibrium behavior of ISs and explore the effects of temperature on the distribution of overlaps and the complexity of the configuration landscape. We introduce an algorithm that allows us to sample ISs accurately and efficiently, enabling us to study large-scale systems and confirm theoretical predictions.
Article
Computer Science, Information Systems
Peter Sussner et al.
Summary: Morphological perceptrons are feedforward morphological neural networks used for classification and regression, with neuronal aggregation functions derived from gray-scale mathematical morphology. The components of MPs compute pair-wise infimum of erosion and anti-dilation, expressed in terms of matrix products in a lattice algebra. This paper introduces the concept of interval descriptor and n-ary aggregation function on a bounded poset to generalize existing components and present examples of generalized morphological components for incorporation into artificial neural networks.
INFORMATION SCIENCES
(2022)
Article
Mathematics, Applied
Janusz Brzdek et al.
Summary: This paper investigates the Ulam stability of a fractional order delayed differential equation. Formulas are provided to generate exact solutions of the equation using functions that only approximately satisfy it. The convergence speed and the distance between the approximate and exact solutions are estimated. Exemplary calculations involving different norms and semigauges are provided to obtain reasonable estimations in specific cases.
RESULTS IN MATHEMATICS
(2022)
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: This paper presents methods for stabilizing pseudostochastic (G(1), G(2))-random operator inequality using a class of stochastic matrix control functions in matrix Menger Banach algebras. The authors provide approximations for stochastic (G(1), G(2))-random operator inequality using both direct and fixed point methods. They also demonstrate the application of stochastic Mittag-Leffler and H-fox control functions in improving the approximation of a random operator inequality.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Physics, Mathematical
Safoura Rezaei Aderyani et al.
Summary: By using the trial equation method and modified trial equation method, the analytical solutions of the conformable time-fractional modified nonlinear Schrodinger equation were found, and numerical results were presented in tables and charts.
ADVANCES IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: We apply CRM based on an alternative FPT to approximate a Delta-Hilfer fractional differential equation. In comparison to the Picard method, we show that the CRM has a better error estimate and provides an economically efficient solution.
Article
Computer Science, Theory & Methods
Safoura Rezaei Aderyani et al.
Summary: In this paper, we stabilize the tri-additive Upsilon-random operator inequality by applying the Radu-Mihet method derived from an alternative FPT, and provide a class of stochastic matrix control functions in matrix MB-algebras. Additionally, we estimate permuting trihomomorphisms and permuting tri-derivations in unital matrix MC-lozenge-algebras and matrix MB-algebras.
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
(2022)
Article
Engineering, Multidisciplinary
Safoura Rezaei Aderyani et al.
Summary: This paper investigates the existence, uniqueness approximation of Xi-Hilfer fractional differential equations, and Hypergeometric stability for both finite and infinite domains using the Cadariu-Radu method derived from the Diaz-Margolis theorem. An example is provided to illustrate the main result for a fractional system.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Engineering, Electrical & Electronic
Safoura Rezaei Aderyani et al.
Summary: By utilizing the FIM and FVM techniques, we obtained analytical solutions for the CTFMNLSE and presented numerical results through tables and charts.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Mathematics, Applied
Yixing Liang et al.
Summary: This paper discusses the exact solutions of linear homogeneous and nonhomogeneous fractional differential equations with double delays. A new concept of double-delayed Mittag-Leffler type matrix function is introduced, and it is applied along with Laplace transform approach to obtain the exact solutions. The solutions are also used to investigate the Hyers-Ulam stability of the system, and an example is provided to illustrate the techniques.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Engineering, Multidisciplinary
Safoura Rezaei Aderyani et al.
Alexandria Engineering Journal
(2022)
Article
Mathematics
Safoura Rezaei Aderyani et al.
Summary: In this study, the existence and uniqueness of solution for certain nonlinear partial differential equations were investigated using an alternative theorem. The Ulam-Hyers-Rassias stability of the solution was also examined. Furthermore, the multiple exp function method was applied to obtain multiple wave solutions of the given nonlinear equations. Numerical results were presented and the advantages and disadvantages of the method were discussed.
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: We introduce a new class of fuzzy control functions and define the concept of matrix-valued fuzzy Mittag-Leffler-Hypergeometric-Wright stability. Then, we apply the Radu-Mihet method to investigate the existence, uniqueness, and stability of a class of P-Hilfer fractional differential equations in matrix-valued fuzzy Banach space. Results for unbounded domains are also presented, along with an example illustrating the Mittag-Leffler-Hypergeometric-Wright stability of a fractional system.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Barakah Almarri et al.
Summary: This article studies linear and nonlinear fractional-delay systems and derives controllability and Hyers-Ulam stability results using the representation of solutions of these systems with the help of their delayed Mittag-Leffler matrix functions. Sufficient and necessary conditions for the controllability of linear fractional-delay systems are provided by introducing a fractional delay Gramian matrix. Furthermore, sufficient conditions of controllability and Hyers-Ulam stability of nonlinear fractional-delay systems are established by applying Krasnoselskii's fixed-point theorem.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: In this study, we investigate the concept of antiderivations in Banach algebras and study multi-super-stability of antiderivations in Banach algebras, associated with functional inequalities.
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: In this article, we employ direct algebraic method and sine-Gordon expansion method to obtain the analytical solutions of the conformable time-fractional modified nonlinear Schrodinger equation, and present the numerical results in tables and charts.
Article
Mathematics, Applied
Safoura Rezaei Aderyani et al.
Summary: This article introduces a class of fuzzy matrix valued control functions and applies the Radu-Mihet method to investigate the UHML stability for a class of xi-Hilfer fractional differential equations in matrix valued fuzzy Banach spaces. An example is provided to illustrate the UHML stability for a fractional system.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Safoura Rezaei Aderyani et al.
Summary: By applying the Cadariu-Radu method derived from the Diaz-Margolis theorem, the study explores the existence, uniqueness, and Gauss hypergeometric stability of Omega-Hilfer fractional differential equations on both compact and unbounded domains. The main results for unbounded domains are then presented, along with an example to illustrate the main result for a fractional system.
Article
Mathematics, Interdisciplinary Applications
Suwardi Annas et al.
CHAOS SOLITONS & FRACTALS
(2020)
Article
Computer Science, Artificial Intelligence
Hassan Noori Esfahani et al.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2019)
