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International Journal of Differential Equations
Scopus
ISSN 1687-9643 · Wiley · 549 articles in the index
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Journal Article
Innovative Approaches in Differential Equation Analysis Using the Enhanced Differential Transform and Homotopy Perturbation Method
Ordinary differential equations (ODEs) are very basic when it comes to modeling dynamic systems in various fields of science and engineering. However, solving high-dimensional, nonlinear, and stiff ODEs is still a major challenge given the limitations of existing numerical methods, which tend to…
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Journal Article
Neuronal Dynamics of an Intrinsically Bursting Neuron Through the Caputo–Fabrizio Fractal–Fractional Hodgkin–Huxley Model
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…
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Journal Article
A Study on Mathematical Modelling of Michaelis–Menten Enzyme Kinetics Using Fractional Derivatives
This article investigates mathematical simulations of Michaelis–Menten kinetics in differential biochemical reactions by implementing fractional derivatives. It establishes numerical computations for the concentrations of enzymes, substrates, inhibitors, products, and several complex intermediates…
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Journal Article
Hybrid Fitted Numerical Scheme for Singularly Perturbed Spatiotemporal Delay Differential Equations
In this study, a hybrid scheme is presented to solve a singularly perturbed time-delay differential equation with a delay and advance term in the spatial variable. The scheme combines the midpoint upwind scheme and the cubic spline difference scheme in the outer and inner layer regions…
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Journal Article
Heterogeneous Media Heat Transfer Simulations Based on 3D-Fractional Parametric Laplace Kernel
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…
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Journal Article
Computational Analysis of Prandtl on the Fluid Relaxation Time Features for the Energy and Concentration Nanomaterial Flow of Motile Microorganisms Induced by a Deformable Sheet With Chemical Reactions
This study investigates the phenomenon of bioconvection in a Darcy–Forchheimer flow of a Prandtl fluid on a stretching sheet, considering dual diffusive processes and incorporating the Cattaneo–Christov heat conduction model. For the conversion of modeled equations to dimensionless, a suitable set…
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Journal Article
A Double Age-Structured Model for Within-Host Malaria Dynamics: Coupling RBC Lifespan and Infection Age
Malaria is one of the most prevalent diseases spread by mosquitoes in tropical and subtropical areas. In this study, we present an age-structured mathematical model for the within-host dynamics of Plasmodium falciparum malaria, employing a dual age-structured partial differential equation (PDE)…
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Journal Article
Boundary Poisson Barriers and a Sharper Continuation Theorem for Li–Lin’s Problem
We sharpen the continuation part of Tang and Tang’s subsupersolution argument for the boundary singular Hardy–Sobolev equation −Δu=−λx−s1up−1+x−s2uq−1 in Ω,u=0 on ∂Ω, with 0∈∂Ω. Their explicit supersolution Mx−α forces the bulk superharmonicity restriction α≤N−2, hence the condition q≤p−s2−s1/N−2…
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Journal Article
Wavelet Collocation Method Based on Biorthogonal Flatlet Multiwavelet and Its Application in Solving the Singular BVPs
The main focus of our work is to provide a computationally efficient approximate algorithm for finding a numerical solution of singular boundary value problems (SBVPs). For this purpose, we apply a biorthogonal flatlet multiwavelet collocation method (BFMCM) to solve numerically. This is performed…
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Journal Article
Thermal Analysis of Boger Nanofluid Dynamics Over Permeable Riga Curved Surface With Particle Deposition: Implications for Solar Energy Applications
Boger fluids have various applications in the scientific and engineering fields, including biomedical engineering, materials sciences, chemical process engineering, and other disciplines. The present study aims to examine the 2-dimensional, steady, incompressible circulation of Boger nanofluids…
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Journal Article
Spline-Based Computational Technique for Singularly Perturbed Fredholm Integro-Differential Problems
In this work, using a spline-based discretization, we develop a computational approach for singularly perturbed Fredholm integro-differential equations. The scheme addresses the challenges of the singular perturbation parameter ϵ through a tension and compression spline technique, coupled with…
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Journal Article
Stability Regions and Bifurcation Analysis of a Delayed Tumor Therapy Model Using Oncolytic Virus
We consider the dynamics of a tumor therapy model using oncolytic viruses with time delay. The model is a two-dimensional system of ordinary differential equations with a delay term that represents the latent period required for viral replication following the infection of tumor cells. Our study…
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Journal Article
Optimal Control Analysis and Simulation of a Mathematical Model for Recurrent Malaria Dynamics via the Caputo Fractional-Order Derivative
The Caputo fractional derivative is employed to investigate the role of memory effects in modeling the transmission dynamics of recurrent malaria in interacting human–vector populations. The model generalizes an existing classical version accounting for the three major forms of recurrent malaria…
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Journal Article
Boundary Value Problems With ψ-Hilfer Fractional Derivative: Existence Theorems in Nonlinear Analysis
This work investigates the existence of infinitely many nontrivial weak solutions to a boundary value problem involving the right-sided and left-sided ψ-Hilfer fractional derivative and ψ-Riemann–Liouville fractional integral operators. Using variational methods and critical point theory, we obtain…
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Journal Article
Size-Selective Threshold Harvesting Under Nonlocal Crowding and Exogenous Recruitment
We propose a nonlinear size-structured fishery model for externally recruited stocks under size-selective harvesting. The population density satisfies a McKendrick–von Foerster transport equation in which growth and natural mortality depend on a nonlocal crowding index, while harvesting acts as a…
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Journal Article
Deterministic and Fractional-Order Modeling of Potato Disease Transmission Dynamics
Potato plant diseases are a significant concern because they reduce crop yields and quality, putting the global food supply at risk. Our goal in developing this deterministic, fractional-order epidemic model is to explain the transmission of these diseases by simulating the interactions between…
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Journal Article
New Perspectives on Nonlinear Time-Fractional Wave Systems: Structural Analysis, Numerical Precision, and Fractional Wave Dynamics
This paper develops a Laplace–Residual Power Series Method (L-RPSM) for solving nonlinear time-fractional wave systems in the Caputo sense. The method combines the Laplace transform with a residual power series expansion to construct approximate analytical solutions, where the coefficients are…
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Journal Article
Global Existence and General Decay of Solutions for a Viscoelastic Marguerre–Vlasov System With Nonlinear Delay Feedback
This work focuses on the viscoelastic Marguerre–Vlasov system defined within a bounded domain, incorporating a delay component in the nonlinear internal feedback mechanism. We demonstrate a global existence theorem through the application of the energy method alongside the Faedo–Galerkin approach…
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Journal Article
Numerical Schemes Based on Splines for Two-Dimensional Singularly Perturbed Elliptic Partial Differential Equations With Mixed Shifts
In this study, we considered a singular perturbation problem of two-dimensional, linear elliptic partial differential equations having both positive and negative shifts in both directions of the reaction terms, whose solution exhibits characteristic boundary layers. The shift terms are approximated…
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Journal Article
A New Computational Method Based on Fractional Integration Operational Matrices for Solving Fractional Integro–Differential Equations
This paper presents a new numerical method for solving fractional integro–differential equations. After introducing the necessary preliminary definitions, fractional integration operational matrices are constructed based on fractional Lagrange functions, employed here as fractional basis functions…