Article
Materials Science, Multidisciplinary
Sumati Kumari Panda, Kottakkaran Sooppy Nisar, Velusamy Vijayakumar, Bipan Hazarika
Summary: This article discusses the existence theory of solutions to fractional differential equations. Existence results have been obtained using various fixed point problems including Lefschetz, Kleene, Tychonoff, and Banach. The article also proposes a generalized version of the contraction principle in the context of controlled rectangular metric space and applies it to discuss the existence and uniqueness results of two fractional-order differential equations.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Dumitru Baleanu, Babak Shiri
Summary: This paper studies the well-posedness of the terminal value problem for nonlinear systems of generalized fractional differential equations. The generalized fractional operator is formulated using a classical operator and a related weighted space. The terminal value problem is transformed into weakly singular Fredholm and Volterra integral equations with delay. A lower bound for the well-posedness is introduced, and a collocation method covering all problems with generalized derivatives is introduced and analyzed. Illustrative examples are provided for validation and application of the proposed methods. The effects of various fractional derivatives on the solution, well-posedness, and fitting error are studied, and an application for estimating the population of diabetes cases in the past is introduced.
Article
Mathematics, Interdisciplinary Applications
Bashir Ahmad, Ahmed Alsaedi, Mokhtar Kirane
Summary: The study demonstrates that solutions to nonlinear equations with distributed fractional derivatives will blow up in a finite time, extending the analysis to a system of nonlinear equations with different orders and weight functions, relying on the non-linear capacity method.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ayub Samadi, Cholticha Nuchpong, Sotiris K. Ntouyas, Jessada Tariboon
Summary: This paper investigates the existence and uniqueness of solutions for a coupled system of psi-Hilfer type sequential fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions. The results are obtained using classical Banach and Krasnosel'skii's fixed point theorems and the Leray-Schauder alternative. Examples are included to demonstrate the effectiveness of the results obtained.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
C. Dineshkumar, R. Udhayakumar, V. Vijayakumar, Kottakkaran Sooppy Nisar
Summary: This manuscript focuses on the approximate controllability of Hilfer fractional neutral stochastic integro-differential equations, proving the principal results based on theoretical concepts related to fractional calculus and Schauder's fixed-point theorem. It discusses the approximate controllability of the fractional evolution system and extends the results to nonlocal conditions. Theoretical and practical applications are provided to enhance the effectiveness of the discussion.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Nemat Nyamoradi, Bashir Ahmad
Summary: This work explores the existence of solutions to a new class of boundary value problems, which consist of a system of nonlinear differential equations with generalized fractional derivative operators of different orders and nonlocal boundary conditions containing Riemann-Stieltjes and generalized fractional integral operators. The study emphasizes that the nonlinearities in the system are of general form, depending on both the unknown functions and their lower order generalized fractional derivatives. The uniqueness of the given problem is proved by applying the Banach contraction mapping principle, and the existence of solutions for the given system is demonstrated using Leray-Schauder alternative. Two concrete examples are provided to illustrate the obtained results.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Arzu Ahmadova, Ismail T. Huseynov, Arran Fernandez, Nazim Mahmudov
Summary: This study on linear systems of fractional differential equations reveals the need to introduce a new type of Mittag-Leffler function involving triple series and construct associated fractional calculus operators to obtain fully closed-form solutions. By comparing the solutions with existing vector-matrix solutions, explicit formulae for the elements of the 2×2 matrix Mittag-Leffler function are derived.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics
Hairong Liu, Xiaoping Yang
Summary: This paper investigates the critical points and level sets of solutions of the Grushin equation in the plane. It proves that the critical points of solutions are isolated with finite multiplicity, and further estimates the number of interior critical points in the Dirichlet boundary value problem.
JOURNAL D ANALYSE MATHEMATIQUE
(2021)
Article
Computer Science, Theory & Methods
Nguyen Dinh Phu, Vasile Lupulescu, Ngo Van Hoa
Summary: This paper explores a class of fuzzy fractional functional differential equations of neutral type. It obtains the existence, uniqueness, and iterative formula in the case of linear equations, and discusses the continuous dependence of solutions on initial data, parameters, and functions. Several examples are provided to illustrate the applications of the results.
FUZZY SETS AND SYSTEMS
(2021)
Review
Mathematics
Oana Brandibur, Roberto Garrappa, Eva Kaslik
Summary: This paper provides a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative, including investigations into single-order systems, multi-order systems, and the role of the Mittag-Leffler function. Numerical experiments are presented to illustrate the main results.
Article
Mathematics, Applied
Abdullahi Yusuf, Bahar Acay, Mustafa Inc
Summary: This study provides a detailed analysis of two crucial real-world problems under the Caputo fractional derivative, utilizing a non-local fractional operator to investigate mathematical models of the planktonic ecosystem and biological system on Planet GLIA-2. The theoretical and numerical results for phytoplankton model highlight its importance in preventing global warming, while the existence and uniqueness of solutions are discussed under the fixed-point theorem. The first-order convergent numerical technique is used to simulate the governing models, demonstrating the conditions for the development of phytoplankton, Jancor, Murrot, and Vekton populations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Sreedharan Raju, Raja Balachandar Sevugan, Ramalingam Udhayakumar, Ghada Alnemer, Umamaheswaran Arunachalam
Summary: This article focuses on the existence, uniqueness, and approximate controllability of solutions for fractional neutral differential equations with deformable derivatives. The findings are achieved through the application of Banach's, Krasnoselskii's, and Schauder's fixed-point theorems, as well as semigroup theory. Three numerical examples are provided to illustrate the practical application of the discussed theories.
FRACTAL AND FRACTIONAL
(2023)
Article
Physics, Multidisciplinary
H. Azin, M. H. Heydari, O. Baghani, F. Mohammadi
Summary: In this study, the fractional Vieta-Fibonacci wavelets are introduced to construct a numerical method for solving a class of fractional delay systems of differential equations. The relationships regarding fractional integration and derivative of these wavelets are extracted, and all unknown functions in the system are then approximated by these wavelets. By substituting these approximations into the system and applying the collocation method, a system of algebraic equations is obtained and solved to determine the unknown coefficients and obtain a solution for the main system. The proposed method is evaluated with solving several examples, and the convergence analysis and error bound for approximation with the fractional Vieta-Fibonacci wavelets are derived.
Article
Mathematics, Applied
Paul Bosch, Jose M. Rodriguez, Jose M. Sigarreta
Summary: In this paper, the authors work with a general formulation of Caputo-type fractional derivative and study oscillatory solutions of differential equations involving these derivatives. They extend the Kamenev-type oscillation criterion proposed by Baleanu et al. in 2015 and prove results on the existence and uniqueness of solutions for many equations. Finally, they provide some examples to enhance their study.
Article
Mathematics, Interdisciplinary Applications
Wang Mei-Qi, Ma Wen-Li, Li Yuan, Chen En-Li, Liu Peng-Fei, Zhang Ming-Zhi
Summary: This paper analyzes a class of piecewise nonlinear systems with fractional differential delay feedback control. The average method is used to solve the nonlinear system and obtain the amplitude-frequency relationship. The correctness of the analytical solution is verified by numerical solution, and the effects of system parameters on the amplitude-frequency characteristics are analyzed. Finally, the dynamic analysis of the system is conducted, and periodic motion, period doubling motion, and chaos are observed with the change of perturbation parameters.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Automation & Control Systems
J. J. Trujillo, V. M. Ungureanu
INTERNATIONAL JOURNAL OF CONTROL
(2018)
Article
Mathematics, Applied
M. Ghasemi, Y. Jalilian, J. J. Trujillo
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2017)
Article
Mathematics, Applied
Mabel Lizzy Rajendran, Krishnan Balachandran, Juan J. Trujillo
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2017)
Article
Mathematics
Maria Pilar Velasco, David Usero, Salvador Jimenez, Luis Vazquez, Jose Luis Vazquez-Poletti, Mina Mortazavi
Article
Engineering, Mechanical
Luis Vazquez, M. Pilar Velasco, Dumitru Baleanu, J. Luis Vazquez-Poletti, Salvador Jimenez
Summary: We describe certain limits associated with the Schrodinger equation, the classical wave equation, and Maxwell equations. These limits are determined by the competition of two fundamental scales. We particularly focus on the competition between an exploratory wavelength and the scale of fluctuations in the propagation media, as well as the propagation of electromagnetic waves in media with self-similar structures. This study requires large-scale computations, which can be achieved in the framework of cloud computing.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
G. Narayanan, M. Syed Ali, Hamed Alsulami, Bashir Ahmad, J. J. Trujillo
Summary: This paper investigates the diffusion effects of mRNA and proteins in genetic regulatory networks and proposes a hybrid impulsive and sampled-data controller. Finite-time stabilization criteria are derived for fractional-order delayed reaction-diffusion genetic regulatory networks (FDRDGRNs) by constructing a suitable Lyapunov functional and utilizing the average impulsive interval approach. The impulsive control gains and sampled-data control gains are obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is presented to demonstrate the applicability of the proposed scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics
Mokhtar Boumaaza, Mouffak Benchohra, Juan J. Trujillo
Summary: In this paper, we investigate the existence of weak solutions for some coupled systems of fractional Caputo-type modification of the Erdelyi-Kober differential equations with retardation and anticipation. Our approach is based on Monch's fixed point theorem associated with the technique of measure of weak noncompactness. Finally, an example of our results is provided.
JORDAN JOURNAL OF MATHEMATICS AND STATISTICS
(2022)
Article
Mathematics, Applied
J. L. Vazquez-Poletti, M. P. Velasco, S. Jimenez, D. Usero, I. M. Llorente, L. Vazquez, O. Korablev, D. Belyaev, M. Patsaeva, I. Khatuntsev
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2019)
Article
Mathematics, Applied
Luciano Abadias, Carlos Lizama, Pedro J. Miana, M. Pilar Velasco
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2019)
Article
Mathematics, Interdisciplinary Applications
Salvador Jimenez, David Usero, Luis Vazquez, Maria Pilar Velasco
FRACTAL AND FRACTIONAL
(2018)
Article
Mathematics, Applied
Luis Vazquez, M. Pilar Velasco, Jose Luis Vazquez-Poletti, Ignacio M. Llorente, David Usero, Salvador Jimenez
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
(2018)
Article
Mathematics
Aruchamy Akilandeeswari, Krishnan Balachandran, Margarita Rivero, Juan J. Trujillo
TBILISI MATHEMATICAL JOURNAL
(2017)
Article
Mathematics
Neda Khodabakhshi, S. Mansour Vaezpour, J. Juan Trujillo
MATHEMATICA SLOVACA
(2017)
Article
Geosciences, Multidisciplinary
Ari-Matti Harri, Konstantin Pichkadze, Lev Zeleny, Luis Vazquez, Walter Schmidt, Sergey Alexashkin, Oleg Korablev, Hector Guerrero, Jyri Heilimo, Mikhail Uspensky, Valery Finchenko, Vyacheslav Linkin, Ignacio Arruego, Maria Genzer, Alexander Lipatov, Jouni Polkko, Mark Paton, Hannu Savijarvi, Harri Haukka, Tero Siili, Vladimir Khovanskov, Boris Ostesko, Andrey Poroshin, Marina Diaz-Michelena, Timo Siikonen, Matti Palin, Viktor Vorontsov, Alexander Polyakov, Francisco Valero, Osku Kemppinen, Jussi Leinonen, Pilar Romero
GEOSCIENTIFIC INSTRUMENTATION METHODS AND DATA SYSTEMS
(2017)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
