Article
Computer Science, Artificial Intelligence
Octavian Postavaru
Summary: In this study, a systematic technique is proposed for solving fractional delay differential equations in the Caputo sense. The proposed method involves computing an exact Riemann-Liouville fractional integral operator for a hybrid of block-pulse functions and Bernoulli polynomials, which allows reducing the equations into a system of algebraic equations. The numerical solution is obtained using Newton's iterative method. The simplicity and accuracy of the method make it superior to other methods presented in the literature for the same problems.
Article
Computer Science, Interdisciplinary Applications
Octavian Postavaru, Antonela Toma
Summary: An accurate and efficient computational method based on a fractional-order hybrid of block-pulse functions and Bernoulli polynomials is presented for solving fractional optimal control problems. By constructing a specific integral operator and transforming the original problem, the method provides accurate results with high computational efficiency.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Computer Science, Interdisciplinary Applications
O. Postavaru, S. R. Anton, A. Toma
Summary: The dynamics of COVID-19 was investigated using a fractional order SEIR model to calculate the number of infections considering chaotic contributions. The model was tested in multiple regions and the results are significant for evidence-based decision making and policy formulation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Bo Zhang, Yinggan Tang, Xuguang Zhang
Summary: A new efficient numerical method for solving FDEs is proposed in this paper, which converts FDEs into a system of algebraic equations using a hybrid Bernoulli polynomials and block pulse functions operational matrix. Simulation examples show that the method is much more efficient and accurate than other known methods.
MATHEMATICAL SCIENCES
(2021)
Article
Mathematics, Applied
Hailun Wang, Fei Wu, Dongge Lei
Summary: This article introduces a novel numerical method for solving fractional order differential equations using hybrid functions, and conducts error analysis of the algorithm. Numerical examples demonstrate the effectiveness of the proposed method.
Article
Mathematics, Applied
Bo Zhang, Yinggan Tang, Xuguang Zhang
Summary: This article introduces an efficient numerical method for solving variable coefficients fractional differential equations. The method combines the characteristics of Bernoulli polynomials and block pulse functions, overcomes the drawbacks of block pulse functions, and can obtain more accurate approximate solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Jie Zhang, Yinggan Tang, Fucai Liu, Zhaopeng Jin, Yao Lu
Summary: A novel numerical method combining block pulse functions and Bernstein polynomials has been proposed to solve fractional differential equations, simplifying the equations into a system of algebraic equations for numerical solution. The convergence analysis of the method has been conducted, showing the validity, applicability, and efficiency of the proposed technique compared to other approaches.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Ravshan Ashurov, Rajapboy Saparbayev
Summary: The Cauchy problem for the telegraph equation with the Caputo derivative and a selfadjoint positive operator is considered. Conditions are found for the existence and uniqueness of the solution. These conditions are less restrictive than expected, as shown in a previous study. Stability estimates important for application are also proven.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Kamal Shah, Rozi Gul
Summary: This work investigates a class of fractional integro-differential equations under Caputo-Fabrizo derivative, establishing existence and uniqueness results using Banach's and Krasnoselskii's fixed point theorems. Necessary conditions for stability analysis are derived, and a relevant problem is provided to illustrate the main results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Raniyah E. Alsulaiman, Mohamed A. Abdou, Mahmoud M. Elborai, Wagdy G. El-Sayed, Eslam M. Youssef, Mai Taha
Summary: In this research, a qualitative analysis is performed for a new modification of a nonlinear hyperbolic fractional integro-differential equation in dual Banach space. The existence and uniqueness of a solution are proven under suitable conditions using fixed-point theorems. The proposed method is verified by applying the Lerch matrix collocation method and comparing the results with other numerical methods.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Fereshteh Saemi, Hamideh Ebrahimi, Mahmoud Shafiee, Kamyar Hosseini
Summary: In this research, a new scheme based on the two-dimensional normalized Muntz-Legendre polynomials (2D-NMLPs) is utilized to study the two-dimensional Volterra-Fredholm integro-differential (2D-VFID) equations of fractional order. The proposed scheme has the advantage that the approximate solution can be expressed in terms of fractional or integer powers. The operational matrices of Riemann-Liouville fractional (RLF) integral and Caputo fractional (CF) derivative are extracted based on the 2D-NMLPs, and the approximate solution of the 2D-VFID equations is constructed by solving the system of linear/nonlinear algebraic equations formed by these operational matrices. The stability, error bound, and convergence of the scheme are discussed in detail, and examples are presented to demonstrate the accuracy of the scheme in handling the 2DVFID equations of fractional order.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Suayip Yuzbasi
Summary: In this study, a collocation method based on the Bell polynomials is introduced for solving linear fractional integro-differential equations. By expressing the fractional Bell functions in matrix forms and using Caputo derivative and equal spacing points, the linear fractional problem is transformed into a system of linear algebraic equations, and its solutions provide the coefficients of the assumed solution.
MATHEMATICAL SCIENCES
(2022)
Article
Mathematics
Taher S. Hassan, Ismoil Odinaev, Rasool Shah, Wajaree Weera
Summary: This article presents a technique for solving fractional integro differential equations using the Chebyshev pseudospectral method. The results demonstrate the high accuracy and reliability of the proposed technique, which is compared to other methods and the exact solution. The Chebyshev pseudospectral method is shown to be more accurate and straightforward compared to other methods.
Article
Mathematics, Applied
Abeer Al Elaiw, Farva Hafeez, Mdi Begum Jeelani, Muath Awadalla, Kinda Abuasbeh
Summary: In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order beta is an element of (1, 2) and gamma is an element of (0, 1). We prove some important results by using integro-differential equation of pantograph type. We establish the existence and uniqueness of the solutions using fixed point theorem. Furthermore, one application is likewise given to represent our fundamental results.
Article
Mathematics, Applied
Raniyah E. Alsulaiman, Mohamed A. Abdou, Eslam M. Youssef, Mai Taha
Summary: Under suitable conditions, the existence and uniqueness of a solution to a modified nonlinear fractional integro-differential equation (NFIDEq) in dual Banach space CE (E, [0, T]) are studied, which has applications in mathematical physics, quantum mechanics, and other domains. The use of fixed-point theorems and the theory of fractional calculus validate the desired conclusions. The Bernoulli matrix approach (BMA) is employed as a numerical method to demonstrate the effectiveness of the provided strategy, offering more precise results compared to other methods.
