Results 81 to 90 of about 7,526 (199)

On solving a singular Volterra integral equation

Filomat
In the paper, a general solution of the singular Volterra integral equation of the second kind is found. The feature of the considered integral equation lies in the fact that the integral of its kernel does not tend to zero as the upper limit approaches the lower one, thus making the Picard method inapplicable.
Murat Ramazanov, Nurtay Kudaybergenovich Gulmanov, Madi Tulegenovich Omarov   +2 more
openaire   +1 more source

Heterogeneous Media Heat Transfer Simulations Based on 3D‐Fractional Parametric Laplace Kernel

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper introduces a new Mittag–Leffler–Laplace memory kernel defined by Φ˜μ,ν,κα,ρs=∫0∞Eρ−μξκ/κξνα−1e−sξdξ, s>0, and develops a unified framework for modeling heat transfer in heterogeneous media with nonlocal temporal memory. The proposed kernel combines algebraic singularity, stretched attenuation, and fractional relaxation through independent ...
Rabha W. Ibrahim, Ali A. Jizany, Hasan Kahtan, Elena Kaikina   +3 more
wiley   +1 more source

A Morgan‐Voyce Polynomial Framework for Solving Variable‐Order Atangana–Baleanu Fractional Differential Equations

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper presents a novel and efficient spectral collocation framework for solving nonlinear variable‐order fractional differential equations (VO‐FDEs) involving the Atangana–Baleanu–Caputo (ABC) operator. Shifted Morgan‐Voyce polynomials (SMVPs) are employed as basic functions to construct a new operational matrix specifically adapted to the ...
Ghadah S. E. Noman, D. D. Pawar, Sining Zheng   +2 more
wiley   +1 more source

Positive solutions of Volterra integral equations using integral inequalities

Journal of Inequalities and Applications, 2002
The existence of positive solutions of certain special cases of the possibly singular Volterra integral equation is discussed, using Krasnoselskii's fixed point theorem.
O'regan Donal, Meehan Maria
doaj  

Solution of a singular integral equation by a split-interval method

, 2007
The article is available at http://www.math.ualberta.ca/ijnam/Volume-4-2007/No-1-07/2007-01-05.pdf. This article is not available through the Chester Digital RepositoryThis article discusses a new numerical method for the solution of a singular integral ...
Diogo, Teresa, Ford, Neville J., Lima, Pedro M., Thomas, Sophy M.   +3 more
core  

Singular optimal control of stochastic Volterra integral equations

, 2019
This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations, where the solution X^{u, }(t)=X(t) is given by X(t) = (t)+\int_{0}^{t}}b(t,s,X(s),u(s)) ds+\int_{0}^{t} (t,s,X(s),u(s))dB(s) +\int _{0}^{t}\int_{0}^{t}h(t,s) d (s).
Agram, Nacira, Labed, Saloua, Øksendal, Bernt, Yakhlef, Samia   +3 more
openaire   +2 more sources

Neuronal Dynamics of an Intrinsically Bursting Neuron Through the Caputo–Fabrizio Fractal–Fractional Hodgkin–Huxley Model

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This study introduces a novel fractal–fractional extension of the Hodgkin–Huxley model to capture complex neuronal dynamics, with particular focus on intrinsically bursting patterns. The key innovation lies in the simultaneous incorporation of Caputo–Fabrizio operators with fractional order α for memory effects and fractal dimension τ for temporal ...
M. J. Islam, M. J. Abedin, A. Hoque, M. G. Hafez, Jaume Giné   +4 more
wiley   +1 more source

Numerical solution methods for viscoelastic orthotropic materials [PDF]

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral ...
Brinson, H. F., Dillard, D. A., Gramoll, K. C.   +2 more
core   +1 more source

A Lucas Operational Matrix Method for Solving Nonlinear Fractional Two‐Dimensional Partial Volterra Integral Equations

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This paper introduces a new numerical method for solving a class of two‐dimensional fractional partial Volterra integral equations (2DFPVIEs). Our approach uses Lucas polynomials (LPs) to construct operational matrices (OMs) that effectively transform the complex fractional‐order equations into a more manageable system of algebraic equations.
S. S. Gholami, A. Ebadian, A. A. Khajehnasiri, Kareem T. Elgindy, Birendra Nath Mandal   +4 more
wiley   +1 more source

Identification of a time-dependent source term in a nonlocal problem for time fractional diffusion equation

Mathematical Modelling and Analysis
This paper is concerned with the inverse problem of recovering the time dependent source term in a time fractional diffusion equation, in the case of nonlocal boundary condition and integral overdetermination condition.
Mansur I. Ismailov, Muhammed Çiçek
doaj   +1 more source