Article
Mathematics, Interdisciplinary Applications
Nezha Maamri, Jean-Claude Trigeassou
Summary: This study demonstrates that the usual approach to integrating fractional order initial value problems may lead to incorrect free-response transients. A new generalized method is proposed and applied to modeling and transient analysis of Fractional Differential Systems.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Chung-Sik Sin, Hyon-Sok Choe, Jin-U Rim
Summary: This paper deals with a multiterm time-fractional partial differential equation involving the Caputo operator associated with the Laplace operator. The equation includes the momentum equations of the fractional Oldroyd-B fluid and the fractional Burgers fluid under suitable conditions. The well-posedness and the long-time behavior for the Dirichlet problem are obtained by utilizing several properties of multivariate Mittag-Leffler functions. Additionally, the uniqueness in the inverse problem of determining the orders of time-fractional derivatives of the equation is proven.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Qinqin Xu, Yuanguo Zhu
Summary: This paper explores competitive failure modes for uncertain random fractional systems involving degradation and shock processes. A wear degradation model is developed using uncertain fractional differential equations to demonstrate the potential heredity and memorability of a system. Three definitions of reliability index for competitive failures are presented and the corresponding formulas are derived. A numerical example confirms the validity of the proposed methods.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ahmad Mugbil, Nasser-Eddine Tatar
Summary: This paper investigates an integro-differential problem involving Hadamard fractional derivatives and proves that solutions asymptotically tend to logarithmic functions under certain reasonable conditions. The approach is based on a generalized version of Bihari-LaSalle inequality.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Jian Wang, Yuanguo Zhu, Yajing Gu, Ziqiang Lu
Summary: This paper focuses on linear uncertain fractional order neutral differential equations, providing analytic solutions using the Mittag-Leffler function and investigating the uncertainty distribution of the solution. The author also discusses the dependence of the solution on the initial function based on the generalized Gronwall inequality.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Hanjie Liu, Yuanguo Zhu, Yiyu Liu
Summary: In this paper, the authors utilize the Caputo-Hadamard uncertain fractional differential equations to simulate the dynamic change of stock price and study the European option pricing problem. They provide pricing formulas for an uncertain stock model with mean-reverting process and consider the impact of uncertain interference on bonds, presenting the corresponding European option pricing formulas. Numerical examples are used to demonstrate the effectiveness of the pricing formulas.
Article
Mathematics, Applied
Mohammed D. Kassim, Mubarak Alqahtani, Nasser-Eddine Tatar, Aymen Laadhari
Summary: In this paper, the nonexistence of nontrivial global solutions is investigated for a class of sequential fractional differential inequalities involving Caputo fractional derivatives with different orders. The investigation is conducted in a suitable space using the test function technique and properties of fractional integrals. Numerical examples are presented to support the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Abdelkrim Salim, Mouffak Benchohra, John R. Graef, Jamal Eddine Lazreg
Summary: This manuscript is dedicated to proving the existence of solutions to a class of initial value problems for nonlinear fractional hybrid implicit differential equations with a psi-Hilfer fractional derivative. The result is based on a fixed point theorem introduced by Dhage. Examples are provided to illustrate the result.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Chenkuan Li, Reza Saadati, Donal O'Regan, Radko Mesiar, Andrii Hrytsenko
Summary: In this paper, a new nonlinear partial integro-differential equation with nonlocal initial value conditions is studied, and the solutions of this equation are investigated. By considering an equivalent implicit integral equation and utilizing Babenko's approach, Banach's contraction principle, and the multivariable Mittag-Leffler function, the uniqueness of solutions of the equation is proven. The application of the key theorem is also demonstrated with an illustrative example.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Ting Jin, Fuzhen Li, Hongjun Peng, Bo Li, Depeng Jiang
Summary: This paper investigates the uncertain barrier swaption pricing problem using the fractional differential equation in Caputo sense and analyzes the efficiency index. It aims to address the limitations of existing models and measure the exercise ability of the barrier swaption pricing model. By introducing the Caputo fractional differential operator, a new uncertain barrier swaption model is established for the floating interest rate. Pricing formulas and efficiency index are derived based on the first hitting time. The rationality of the model is verified through numerical examples.
Article
Mathematics, Interdisciplinary Applications
Shuqin Zhang, Xinwei Su
Summary: This paper deals with the unique existence of solution to initial value problem for fractional differential equation involving with fractional derivative of variable order, and provides some examples to substantiate these theoretical results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Yiyu Liu, Yuanguo Zhu, Ziciiang Lu
Summary: This paper focuses on the tool of uncertain fractional differential equations (UFDEs) for describing the behavior of complex systems with memory effects in uncertain environments. Specifically, it investigates the Caputo-Hadamard UFDEs, proposing their definition, providing analytical solutions for linear Caputo-Hadamard UFDEs, and studying the existence and uniqueness theorem for solutions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ziqiang Lu, Yuanguo Zhu, Qinyun Lu
Summary: This paper investigates the stability problems for Caputo type of uncertain fractional differential equations with the order 0 < p <= 1 driven by Liu process, proposing a concept of stability in measure of solutions and deriving several sufficient conditions for stability in two different order cases. Illustrative examples are performed to demonstrate the effectiveness of the proposed results.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Applied
Ho Vu, John M. Rassias, Ngo Van Hoa
Summary: The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) using the concept of Caputo fractional derivative. The existence and uniqueness of solutions for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. New sufficient conditions for ensuring the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of BVP-FDEs are also provided.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Monireh Nosrati Sahlan, Hojjat Afshari, Jehad Alzabut, Ghada Alobaidi
Summary: In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and utilized to evaluate the numerical solution of the Caputo fractional order diffusion wave equations. Galerkin and collocation spectral methods are employed to solve the nonlinear fractional problem. The presented method demonstrates high accuracy and advantages of having compact support and orthogonality, leading to sparse operational matrices and reduced computational time and CPU requirements.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Ibrahim Slimane, Zoubir Dahmani, Juan J. Nieto, Thabet Abdeljawad
Summary: This paper discusses a nonlinear hybrid differential equation written using a fractional derivative with a Mittag-Leffler kernel. The existence of solutions to the problem is established using the Banach contraction theorem, and the existence of mild solutions is discussed using the Dhage fixed-point principle. Additionally, the Ulam-Hyers stability of the introduced fractional hybrid problem is studied.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Israr Ahmad, Hussam Alrabaiah, Kamal Shah, Juan J. Nieto, Ibrahim Mahariq, Ghaus Ur Rahman
Summary: A qualitative analysis for a nonlinear system of fractional pantograph evolution differential equations (FPEDEs) is established in this paper, considering the conditions for the existence and uniqueness of the solutions. By utilizing the fixed-point theorems and tools of nonlinear analysis, the required results are obtained. To confirm the reliability of the obtained results, relevant examples are provided.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Automation & Control Systems
Rohit Patel, V. Vijayakumar, Juan J. Nieto, Shimpi Singh Jadon, Anurag Shukla
Summary: This article investigates the optimal control problem of a mixed Volterra-Fredholm-type third-order dispersion system, proving the existence and uniqueness of mild solution, optimal control, and time-optimal control. The time-optimal control of the third-order dispersion system is also discussed.
ASIAN JOURNAL OF CONTROL
(2023)
Article
Mathematical & Computational Biology
Ibrahim Slimane, Ghazala Nazir, Juan J. Nieto, Faheem Yaqoob
Summary: In this paper, a mathematical model of Hepatitis C Virus (HCV) infection is studied. The existence, uniqueness, and stability of the system are proven and its qualitative properties are analyzed. Additionally, a semi-analytical solution of the model is obtained using the Laplace Adomian decomposition method. Numerical simulations and graphs are presented to illustrate the properties of the solutions.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2023)
Article
Mathematics
Guotao Wang, Yuchuan Liu, Juan J. Nieto, Lihong Zhang
Summary: In this article, the parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity is studied using the direct method of moving planes. Several important theorems are proven, such as the asymptotic maximum principle, asymptotic narrow region principle, and asymptotic strong maximum principle for antisymmetric functions, which are critical in the process of moving planes. Additionally, properties of the asymptotic radial solution in a unit ball are derived, which can be applied to investigate more nonlinear nonlocal parabolic equations.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics
Armin Hadjian, Juan J. Nieto
Summary: In this paper, a local minimum result of differentiable functionals is used to demonstrate the existence of a non-trivial weak solution for a perturbed Dirichlet boundary value problem with a Lipschitz continuous non-linear term, under an asymptotical behavior of the nonlinear datum at zero. Furthermore, special cases and a concrete example of an application are presented.
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
(2023)
Article
Mathematics, Applied
Saad Ihsan Butt, Iram Javed, Praveen Agarwal, Juan J. Nieto
Summary: In this article, the construction of fractional Newton-Simpson-type inequalities using majorization is the main objective. A new identity for estimates of definite integrals is established through majorization, leading to the development of new generalized forms of prior estimates. Various basic inequalities such as Holder's, power-mean, Young's, and the Niezgoda-Jensen-Mercer inequality are used to obtain new bounds, which are found to be generalizations of many existing results in the literature. Applications to the quadrature rule are also provided, along with connections to several well-known discoveries in the literature.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Subhas Khajanchi, Mrinmoy Sardar, Juan J. Nieto
Summary: This article primarily investigates the implicit analytical solutions of a tumor cell population differential equation with a strong Allee effect. Both the ordinary case and a fractional version are considered, and some particular cases are plotted.
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Jia-Li Wei, Guo-Cheng Wu, Bao-Qing Liu, Juan J. Nieto
Summary: This paper proposes a multi-layer neural network for deep learning based on fractional differential equations, and uses parallel computing to search for an optimal structure. The Caputo derivative is approximated by L1 numerical scheme, and an unconstrained discretization minimization problem is presented. The efficiency of the method is demonstrated through analytical approximate solutions of two fractional logistic equations (FLEs). Furthermore, the fractional order and other parameters of FLEs are estimated using the gradient descent algorithm, and the proposed optimal NN method is used for forecasting. Comparative studies show that FLEs have more parameter freedom degrees and outperform the classical logistic model.
NEURAL COMPUTING & APPLICATIONS
(2023)
Article
Mathematics, Applied
Ravikumar Kasinathan, Ramkumar Kasinathan, Varshini Sandrasekaran, Juan J. Nieto
Summary: In this paper, the existence and stability of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups in Hilbert spaces are investigated using resolvent operators. The existence of mild solution is proved by utilizing Monch fixed point theorem and considering the Hausdorff measures of noncompactness. The stability results include continuous dependence of solutions on initial conditions, exponential stability, and Hyers-Ulam stability for the aforementioned system. An example is provided to demonstrate the obtained results.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ivan Area, Juan J. J. Nieto
Summary: This paper studies a quadratic nonlinear equation from the fractional point of view and provides an explicit solution using the Lambert special function. It reveals a new phenomenon involving the collapsing of the solution and the blow-up of the derivative. The explicit representation of the solution shows the non-elementary nature of the solution.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
K. Kaliraj, P. K. Lakshmi Priya, Juan J. Nieto
Summary: This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the delayed-type matrix Mittag-Leffler function. The existence and uniqueness of the solution for the considered fractional model are discussed first. Then, the standard form of integral inequality of Gronwall's type is used along with the application of the delayed Mittag-Leffler argument to derive the sufficient bounds for the stability of the dynamical system. The analysis of the system is extended and studied with impulsive perturbations, and numerical simulations are illustrated using relevant examples.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Abdelhamid Bensalem, Abdelkrim Salim, Mouffak Benchohra, Juan J. Nieto
Summary: The purpose of this study is to investigate the existence and controllability of a mild solution to a second-order semilinear integro-differential problem using resolvent operators. A criterion is constructed using a fixed point theorem and measures of noncompactness. The obtained results are illustrated with a practical example.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2023)
Article
Mathematical & Computational Biology
Nandhini Mohankumar, Lavanya Rajagopal, Juan J. Nieto
Summary: In this paper, a mathematical model is proposed to study the co-infection of COVID-19-Associated Pulmonary Aspergillosis (CAPA) and investigate the relationship between prevention and treatment. The co-infection model is enhanced by incorporating time-dependent controls as interventions based on Pontryagin's maximum principle to obtain the necessary conditions for optimal control. Numerical experiments with different control groups are performed to evaluate the elimination of infection. The results show that transmission prevention control, treatment controls, and environmental disinfection control provide the best chance of preventing the spread of diseases more rapidly than any other combination of controls.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Quantum Science & Technology
Sajede Harraz, Shuang Cong, Juan J. Nieto
Summary: In this paper, a tripartite teleportation protocol is proposed to transmit an unknown quantum state via noisy quantum channels with fidelity equal to one, even with a non-maximally entangled state. The protocol utilizes environment-assisted measurement during entanglement distribution and modifies the standard teleportation protocol by applying weak measurement reversal in the final step. Weak measurement reversal operators are designed to ensure teleportation fidelity equal to one, regardless of decoherence magnitude or shared entangled state parameters. The detailed procedure of the standard tripartite teleportation protocol in the presence of amplitude damping is provided, and the final expression of the average standard teleportation fidelity is derived.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Mathematics, Applied
Guglielmo Feltrin, Maurizio Garrione
Summary: This article deals with a non-autonomous parameter-dependent second-order differential equation driven by a Minkowski-curvature operator. It proves the existence of strictly increasing heteroclinic solutions and homoclinic solutions with a unique change of monotonicity under suitable assumptions, and analyzes the asymptotic behavior of these solutions.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Mehraj Ahmad Lone, Idrees Fayaz Harry
Summary: In this paper, we study Lorentzian generalized Sasakian space forms admitting Ricci soliton, conformal gradient Ricci soliton, and Ricci Yamabe soliton. We also investigate the conditions for solitons to be steady, shrinking, and expanding. Additionally, we provide applications of Ricci Yamabe solitons.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhihao Lu
Summary: We present a unified method for deriving differential Harnack inequalities for positive solutions to semilinear parabolic equations, subject to an integral curvature condition, on compact manifolds and complete Riemannian manifolds. In addition to the case of scalar equations, we also establish an elliptic estimate for the heat flow under the same condition, which is a novel result for both harmonic map and heat equations.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giuseppe Cosma Brusca
Summary: We investigate the asymptotic behavior of the minimal heterogeneous d-capacity of a small set in a fixed bounded open set Omega. We prove that this capacity is related to the parameter lambda and behaves as C |log epsilon|^(1-d), where C is a constant.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Stefan Schiffer
Summary: This note investigates the complex constant rank condition for differential operators and its implications for coercive differential inequalities. Depending on the order of the operators, such inequalities can be viewed as generalizations of either Korn's inequality or Sobolev's inequality.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Konstantinos T. Gkikas, Phuoc-Tai Nguyen
Summary: This article studies the boundary value problem with an inverse-square potential and measure data. By analyzing the Green kernel and Martin kernel and using appropriate capacities, necessary and sufficient conditions for the existence of a solution are established in different cases.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giovanni Bellettini, Simone Carano, Riccardo Scala
Summary: This article computes the relaxed Cartesian area in the strict BV-convergence for a class of piecewise Lipschitz maps from the plane to the plane, where the jump is composed of multiple curves that are allowed to meet at a finite number of junction points. It is shown that the domain of this relaxed area is strictly contained within the domain of the classical L1-relaxed area.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng, Jeremy Sok
Summary: In this paper, we establish the well-posedness of a perturbed Dirac equation with a moving potential W satisfying the Klein-Gordon equation. This serves as a toy model for atoms with relativistic corrections, where the wave function of electrons interacts with an electric field generated by a nucleus with a given charge density. A key contribution of this paper is the development of a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation, which is of independent interest.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Jingwen Chen
Summary: In this article, the authors generalize their previous results to higher dimensions and prove the existence of eternal weak mean root 1 root-1 curvature flows connecting a Clifford hypersurface to the equatorial spheres.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Samuel Borza, Wilhelm Klingenberg
Summary: This article proves that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points, and characterizes conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of the space.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Christina Sormani, Wenchuan Tian, Changliang Wang
Summary: This article presents a sequence of warped product manifolds that satisfy certain hypotheses and proves that this sequence converges in a weak sense to a limit space with nonnegative scalar curvature.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gianni Dal Maso, Davide Donati
Summary: In this paper, we study the F-limits of sequences of quadratic functionals and bounded linear functionals on the Sobolev space, and show that their limits can always be expressed as the sum of a quadratic functional, a linear functional, and a non-positive constant. Furthermore, we prove that the coefficients of the quadratic and linear parts in the Gamma-limit are independent of Omega, and introduce an example to demonstrate that the previous results cannot be generalized to every bounded open set.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Laura Abatangelo, Corentin Lena, Paolo Musolino
Summary: The paper provides a full series expansion of a generalization of the u-capacity related to the Dirichlet-Laplacian in dimension three and higher. The results extend the previous findings on the planar case and are applied to study the asymptotic behavior of perturbed eigenvalues when Dirichlet conditions are imposed on a small regular subset of the domain.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gustavo de Paula Ramos
Summary: This paper employs the photography method to estimate the number of solutions to a nonlinear elliptic problem on a Riemannian orbifold, based on the Lusternik-Schnirelmann category of its submanifold of points with the largest local group.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Tim Espin, Aram Karakhanyan
Summary: This article discusses smooth solutions of the Monge-Ampere equation on an annular domain with two smooth, closed, strictly convex hypersurfaces as boundaries, subject to mixed boundary conditions. It is demonstrated that global C2 estimates cannot be obtained in general unless additional restrictions are imposed on the principal curvatures of the inner boundary and the Neumann condition itself, as shown by an explicit counterexample. Under these conditions, a priori C2 estimates are proven and it is shown that the problem has a smooth solution.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
