Results 81 to 90 of about 6,585 (218)

Solvability of Implicit Fractional Systems With Nonlocal Conditions in Weighted Functional Spaces

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
This paper investigates the existence and uniqueness of solutions for a class of nonlinear implicit Riemann–Liouville fractional integro‐differential equations subject to nonlocal conditions in a weighted Banach space. The inclusion of both implicit effects and nonlocal terms introduces additional complexity, making the analysis both challenging and ...
Abdulrahman A. Sharif, Maha M. Hamood, Kirtiwant P. Ghadle, Sining Zheng   +3 more
wiley   +1 more source

Approximate Solution of Intuitionistic Fuzzy Volterra Integral Equation of Separable‐Type Kernel Using Elzaki Adomian Decomposition Method

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
An intuitionistic fuzzy number, which incorporates both membership and nonmembership functions at a same time, allows for a more accurate representation of uncertainty. This work presents an approximate solution to the Volterra integral equation that involves both membership and nonmembership degrees of uncertainty named as intuitionistic fuzzy ...
Zain Khan, Saleem Abdullah, Samuel Okyere, Bikash Koli Dey   +3 more
wiley   +1 more source

Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations [PDF]

, 2009
Due to the ability of function representation, hybrid functions and wavelets have a special position in research. In this thesis, we state elementary definitions, then we introduce hybrid functions and some wavelets such as Haar, Daubechies, Cheby ...
Vahdati, Saeed
core  

An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions
Shabaz Jalil Mohammedfaeq, Miran Bayan Mohammed Amin, Dashne Chapuk Zahir, Shazad Shawki Ahmed, Saeid Abbasbandy   +4 more
wiley   +1 more source

A Projection Method for Solving Nonlinear Volterra-Fredholm Integral Equations using Legendre Hybrid Functions

Journal of Mathematical Extension, 2013
Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them.
M. Roodaki, Z. JafariBehbahani
doaj  

An Analytical‐Numerical Method for the Solution of Nonlinear Fractional Fredholm Integro‐Differential Equations With Logarithmic Weakly Singular Kernel

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this work, we investigate a numerical method for solving nonlinear fractional Fredholm integro‐differential equations with logarithmic weakly singular kernels. Since the direct solution of these equations using classical methods results in low accuracy and high computational cost due to the singular behavior of the exact solution at both endpoints ...
Ali Edham Awadh, Esmaeil Najafi, Guotao Wang   +2 more
wiley   +1 more source

Fredholm and Volterra Integral Equations of the Second Kind [PDF]

, 1990
Integral equations are often the best way to formulate physics problems. However, the typical physics student gets almost no training in integral equations, in contrast to differential equations, for example.
Press, William H., Teukolsky, Saul A.
core  

Estimates on some power nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales

Advances in Difference Equations, 2017
In this paper, some explicit bounds on solutions to a class of new power nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales are established, which can be used as effective tools in the study of certain dynamic equations ...
Jiangfeng Wang, Fanwei Meng, Juan Gu
doaj   +1 more source

Existence and optimal control results for Caputo fractional delay Clark's subdifferential inclusions of order r∈(1,2) with sectorial operators

Optimal Control Applications and Methods, Volume 45, Issue 4, Page 1832-1850, July/August 2024.
The graphical abstract delves into Caputo fractional nonlinear differential inclusions, highlighting their complexities and the need for innovative solutions. We propose a mild solution approach to address these challenges efficiently. Our investigation focuses on determining the existence of mild solutions under varied conditions and exploring optimal
Marimuthu Mohan Raja, Velusamy Vijayakumar, Kalyana Chakravarthy Veluvolu, Anurag Shukla, Kottakkaran Sooppy Nisar   +4 more
wiley   +1 more source

Analysis of Random Difference Equations Using the Differential Transformation Method

Journal of Applied Mathematics, Volume 2024, Issue 1, 2024.
The differential transformation method (DTM) is one of the best methods easily applied to linear and nonlinear difference equations with random coefficients. In this study, we apply the theorems related to the DTM to the given examples and investigate the behaviour of the approximate analytical solutions.
Şeyma Şişman, Mehmet Merdan, Yansheng Liu   +2 more
wiley   +1 more source