Article
Mathematics, Applied
Ahmed Alsaedi, Bashir Ahmad, Manal Alblewi, Sotiris K. Ntouyas
Summary: This study investigates the existence of solutions for integro-multipoint boundary value problems involving nonlinear multi-term fractional integro-differential equations, with a brief description of the case involving three different types of nonlinearities; the desired results are obtained by applying the methods of modern functional analysis and are well-illustrated with examples.
Article
Mathematics, Interdisciplinary Applications
Gabor Maros, Ferenc Izsak
Summary: The numerical solution of fractional-order elliptic problems in bounded domains with inhomogeneous boundary terms and the full-space fractional Laplacian operator is investigated. Convergence analysis for a lower-order boundary element approximation is based on theory for the corresponding continuous problem. Results are confirmed in a numerical experiment.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Barbara Lupinska
Summary: In this paper, we discuss the existence and uniqueness of solutions for a class of nonlinear fractional differential equations with mixed fractional boundary values using the Banach fixed-point theorem. Additionally, we compare our results with two other works that consider similar problems.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Bashir Ahmad, Sotiris K. Ntouyas
Summary: This paper investigates the existence and uniqueness of solutions for a Hilfer-Hadamard fractional differential equation, using various theorems to establish the existence results and demonstrating the application of the main results through numerical examples. The paper also derives the existence results for problems involving convex and non-convex multifunctions.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Dumitru Baleanu, Babak Shiri
Summary: This paper studies the terminal value problems for systems of fractional differential equations, with a particular focus on higher-order systems. Discretized piecewise polynomial collocation methods are used to approximate the exact solution, leading to a system of nonlinear equations. An iterative method with a required tolerance is introduced and analyzed for solving this system. The existence of a unique solution is guaranteed using the fixed point theorem, and the order of convergence for the numerical method is obtained. Numerical experiments are provided to support the theoretical results.
Article
Mathematics, Applied
Akbar Zada, Mehboob Alam, Usman Riaz
Summary: In this article, implicit q-fractional differential equations involving Stieltjes integral and its corresponding coupled system are analyzed. The existence and uniqueness results for the given problems are obtained by using the Banach contraction principle, Schaefer's fixed point theorem, and Leray-Schauder result of cone type. Various types of stability such as Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability, and generalized Hyers-Ulam-Rassias stability are presented using classical techniques of functional analysis, and the results are verified with examples.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Computer Science, Information Systems
R. Beigmohamadi, A. Khastan, J. J. Nieto, R. Rodriguez-Lopez
Summary: In this study, we introduce discrete interval fractional difference equations subject to non-periodic boundary conditions and obtain two types of solutions for these problems under the generalized Hukuhara difference. We then provide explicit expressions of each type of solution for convenience. Further, we investigate the necessary and sufficient conditions for the existence and uniqueness of a non-periodic solution of each specific type using the Banach contraction mapping principle. Finally, we provide an example to illustrate the main result.
INFORMATION SCIENCES
(2023)
Article
Mathematics, Applied
Yige Zhao
Summary: This article studies the existence result for periodic boundary value problems of nonlinear fractional hybrid differential equations, obtaining the result through Krasnoselskii's fixed point theorem and providing an example to verify it, while also correcting and revising previous statements in Li et al. (2019).
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ananta Thakur, Javid Ali, Rosana Rodriguez-Lopez
Summary: This paper investigates the existence of positive solutions for a class of fractional differential equations of arbitrary order delta > 2, subject to boundary conditions that include an integral operator of the fractional type. An existence result is obtained for the sublinear and superlinear case using the Guo-Krasnosel'skii fixed point theorem, with additional tools such as the explicit expression of Green's function and the study of its properties. An example is provided for illustration of the results.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Ymnah Alruwaily, Bashir Ahmad, Sotiris K. Ntouyas, Ahmed S. M. Alzaidi
Summary: This paper investigates the existence of solutions for a fully coupled Riemann-Stieltjes, integro-multipoint, boundary value problem of Caputo-type sequential fractional differential equations. The given system is studied using the Leray-Schauder alternative and contraction mapping principle. A numerical example is also provided to illustrate the abstract results.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Jie Yang, Guoping Chen
Summary: The paper investigates the existence of solutions for impulsive mixed boundary value problems involving Caputo fractional derivatives, with conclusions drawn from Krasnoselskii's fixed point theorem and Arzela-Ascoli theorem. Several examples are provided to illustrate the main results obtained.
Article
Mathematics, Interdisciplinary Applications
Ravi P. Agarwal, Hana Al-Hutami, Bashir Ahmad
Summary: We present a new class of boundary value problems involving a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. By utilizing standard fixed-point theorems, we establish the existence and uniqueness results for the given problem. We also provide illustrative examples for the obtained results.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas, Bashir Ahmad
Summary: This paper investigates nonlinear fractional (p,q)-difference equations with separated nonlocal boundary conditions. The existence of solutions is proven using Krasnoselskii's fixed-point theorem and the Leray-Schauder alternative, while the uniqueness of solutions is established through Banach's contraction mapping principle. Examples are provided to illustrate the main results.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Manochehr Kazemi, Amar Deep, Juan Nieto
Summary: By utilizing Petryshyn's fixed point theorem in Banach algebra, we investigate the existence of solutions for fractional integral equations, which encompass various fractional integral equations in mathematical analysis and their applications. Moreover, we employ the numerical iterative method to successfully obtain the solutions for these equations. Lastly, we provide several cases and examples to validate the applicability of our study.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Ravi P. Agarwal, Bashir Ahmad, Hana Al-Hutami, Ahmed Alsaedi
Summary: This paper addresses the existence of solutions for a nonlinear multi-term impulsive fractional q-integro-difference equation with nonlocal boundary conditions. The appropriated fixed point theorems are utilized to establish the existence and uniqueness results for the given problem. The obtained results are illustrated through examples.
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
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
Santosh Kumar Sharma, Amar Nath Chatterjee, Bashir Ahmad
Summary: The study focuses on the effects of antiviral therapy on Hepatitis C Virus (HCV) infection. HCV infection damages healthy hepatocyte cells in the liver, leading to cirrhosis and hepatocellular carcinoma. A cell-population model is introduced to understand the long-term dynamics of HCV infection under antiviral drug therapies. The model considers the interactions between susceptible hepatocytes, infected hepatocytes, and HCV to provide a comprehensive understanding of the host dynamics.
Article
Mathematics, Applied
Nattapong Kamsrisuk, Sotiris K. Ntouyas, Bashir Ahmad, Ayub Samadi, Jessada Tariboon
Summary: In this paper, we investigate the existence and uniqueness of solutions to a nonlinear coupled systems of (k,phi)-Hilfer fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while the existence results are proved with the aid of Krasnosel'skii's fixed point theorem and Leray-Schauder alternative for the given problem. Examples demonstrating the application of the abstract results are also presented. Our results are of quite general nature and specialize in several new results for appropriate values of the parameters beta(1), beta(2), and the function ' involved in the problem at hand.
Article
Mathematics, Applied
Pegah Taghiei Karaji, Nemat Nyamoradi, Bashir Ahmad
Summary: In this paper, the SIR model with a nonlinear incidence rate is studied. The disease-free equilibrium E0, the endemic equilibrium E1, and the basic reproduction number R0 of the model are obtained. The local asymptotic stability of E0 is established when R0<1, and the local asymptotic stability of E1 is proved when R0>1. The global stability of the model is studied using Barbalat's lemma. The transcritical bifurcation analysis is investigated by the Sotomayor theorem. The existence of Hopf bifurcation and the sensitivity analysis of the basic reproduction number are checked. Numerical simulations are conducted to support the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(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
Bashir Ahmad, Shorog Aljoudi
Summary: This article investigates the existence criteria for solutions of a nonlinear coupled system of Hilfer-Hadamard fractional differential equations of different orders complemented with nonlocal coupled Hadamard fractional integral boundary conditions. The desired results are achieved using standard fixed-point theorems. The fixed point approach is highlighted as one of the effective methods to establish the existence results for boundary value problems. Examples illustrating the obtained results are provided.
FRACTAL AND FRACTIONAL
(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
Ahmed Alsaedi, Hana Al-Hutami, Bashir Ahmad
Summary: In this paper, a new class of nonlinear multi-term impulsive anti-periodic boundary value problems involving Caputo type fractional q-derivative operators of different orders and the Riemann-Liouville fractional q-integral operator is introduced and investigated. The uniqueness of solutions to the given problem is proved with the aid of Banach's fixed point theorem. An existence result for the problem is also obtained by applying a Shaefer-like fixed point theorem. Examples are constructed to illustrate the obtained results.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Computer Science, Information Systems
R. Beigmohamadi, A. Khastan, J. J. Nieto, R. Rodriguez-Lopez
Summary: In this study, we introduce discrete interval fractional difference equations subject to non-periodic boundary conditions and obtain two types of solutions for these problems under the generalized Hukuhara difference. We then provide explicit expressions of each type of solution for convenience. Further, we investigate the necessary and sufficient conditions for the existence and uniqueness of a non-periodic solution of each specific type using the Banach contraction mapping principle. Finally, we provide an example to illustrate the main result.
INFORMATION SCIENCES
(2023)
Article
Automation & Control Systems
Ahmed Alsaedi, Jinde Cao, Bashir Ahmad, Ahmed Alshehri, Xuegang Tan
Summary: This article proposes a distributed adaptive control scheme for second-order leader-following multiagent systems with only position information as output. An auxiliary network is used to estimate unmeasurable velocity information and make the output-based distributed adaptive control protocol effective. The distributed synchronization criteria are established, and the convergence analysis is provided based on the stability theory. Several simulation examples are presented to validate the proposed criteria.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(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)
