{"title":"Hyers–Ulam stability of Nipah virus model using Atangana–Baleanu–Caputo fractional derivative with fixed point method","authors":"","doi":"10.1016/j.padiff.2024.100939","DOIUrl":"10.1016/j.padiff.2024.100939","url":null,"abstract":"<div><div>In this study, we present a novel investigation into the dynamics of the Nipah virus through the lens of fractional differential equations (FDEs), employing the Atangana–Baleanu–Caputo fractional derivative (ABCFD) and the fixed-point approach (FPA). The core contribution of this work lies in establishing the existence and uniqueness of solutions to the proposed FDEs, a critical step for validating the model. Furthermore, we explore the Hyers–Ulam (HU) stability of these generalized FDEs, providing a rigorous mathematical foundation for the stability analysis within the context of viral dynamics. By leveraging the ABCFD, our work extends the classical stability criteria, offering new insights into the role of memory effects in disease modeling. Additionally, we present approximate solutions across various compartments and fractional orders, highlighting the sensitivity of the system to key parameters. Numerical simulations, conducted using the Cullis method, illustrate the impact of fractional orders and validate the theoretical findings, positioning this work as a significant advancement in the application of fractional calculus to epidemiological models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamical behavior of tempered φ-Caputo type fractional order stochastic differential equations driven by Lévy noise","authors":"","doi":"10.1016/j.padiff.2024.100938","DOIUrl":"10.1016/j.padiff.2024.100938","url":null,"abstract":"<div><div>This paper focuses on the analysis of a class of stochastic differential equations with tempered <span><math><mi>φ</mi></math></span>-Caputo fractional derivative (<span><math><mi>φ</mi></math></span>-CFD) and Lévy noise. We propose comprehensive mathematical techniques to address the existence, uniqueness and stability of solution to this equation. For existence and uniqueness, the Picard–Lindelof successive approximation technique is used analyze the results. Also, We use Mittag-Leffler (M-L) function to investigate the stability of the solution. This research applies the broad understanding of stochastic processes and fractional differential equations, as well as known results, to the analysis of systems with tempered <span><math><mi>φ</mi></math></span>-CFD. These equations capture complex phenomena in the field of financial assets, making their investigation on the stock prices particularly valuable.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity","authors":"","doi":"10.1016/j.padiff.2024.100934","DOIUrl":"10.1016/j.padiff.2024.100934","url":null,"abstract":"<div><div>In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mathematical analysis of soliton solutions in space-time fractional Klein-Gordon model with generalized exponential rational function method","authors":"","doi":"10.1016/j.padiff.2024.100942","DOIUrl":"10.1016/j.padiff.2024.100942","url":null,"abstract":"<div><div>In this article, we investigate the space-time Klein-Gordon (KG) model, a significant framework in quantum field theory and quantum mechanics, which also describes phenomena such as wave propagation in crystal dislocations. This model is particularly important in high-energy particle physics. The novelty of this article is to examine the sufficient, useful in optical fibers, and further general soliton solutions of the nonlinear KG model using the generalized exponential rational function method (GERFM), which do not exist in the recent literature. The fractional complex wave transformation is utilized to turn the model into a nonlinear form, and the accuracy of the acquired solutions is confirmed by reintroducing them into the original models using Mathematica. The obtained solutions are expressed in hyperbolic, exponential, rational, and trigonometric forms. We elucidate the fractional effects for specific parameter values, accompanied by illustrative figures. Our results demonstrate that GERFM is effective, powerful, and versatile, providing exact traveling wave solutions for various nonlinear models in engineering and mathematical physics. Our findings reveal that the characteristics of soliton-shaped waves in both three-dimensional and two-dimensional contexts are profoundly influenced by fractional order derivative. This study advances the understanding of nonlinear wave dynamics and offers a robust method for solving complex physical models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlinear dynamics model of HIV/AIDS: Assessing the impacts of condoms, vaginal microbicides, and optimized treatment","authors":"","doi":"10.1016/j.padiff.2024.100933","DOIUrl":"10.1016/j.padiff.2024.100933","url":null,"abstract":"<div><div>HIV/AIDS remains one of the main global causes of morbidity and mortality. While antiretroviral drugs are still the only treatment for HIV patients, their accessibility and efficient delivery in resource-poor nations constitute a major concern, and no epidemiological model has considered this. Based on this, we create a model for HIV/AIDS that considers condoms and vaginal microbicides alongside saturated treatment. We consider the constant control case, in which theoretical results show that the delay factor in the antiretroviral therapy (ART) regimen can induce backward bifurcation, which consequently distorts the global effort to end HIV incidence. We use the Castillo-Chavez stability to ensure that the disease-free equilibrium is globally asymptotically stable whenever the associated reproduction number is less than one. Uncertainty and sensitivity analysis using the Latin hypercube sampling technique was also carried out on the parameters and state variables of the model equations, and the result shows that half of the most highly influential parameters are capable of reducing cases of HIV and AIDS. For time-dependent control cases, our findings suggest that, in countries with low income, directing resources to either condom use or vaginal microbicides is more effective than a regular intake of antiretrovirals alone. Furthermore, results without ART delay have shown to be more effective in HIV control than others where the inaccessibility of the therapy encouraged outbursts of AIDS cases. Thus, as reliable as antiretrovirals are in HIV/AIDS treatment, early administration and regular intake are key to their continued success.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computational precision in time fractional PDEs: Euler wavelets and novel numerical techniques","authors":"","doi":"10.1016/j.padiff.2024.100918","DOIUrl":"10.1016/j.padiff.2024.100918","url":null,"abstract":"<div><div>This paper presents innovative numerical methodologies designed to solve challenging time fractional partial differential equations, with a focus on the Burgers’, Fisher–KPP, and nonlinear Schrödinger equations. By employing advanced wavelet techniques integrated with fractional calculus, we achieve highly accurate solutions, surpassing conventional methods with minimal absolute error in numerical simulations. A thorough series of numerical experiments validates the robustness and effectiveness of our approach across various parameter regimes and initial conditions. The results underscore significant advancements in the computational modeling of complex physical phenomena governed by time fractional dynamics and offering a powerful tool for a wide range of applications in science and engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Entropy analysis in magnetized blood-based hybrid nanofluid flow via parallel disks","authors":"","doi":"10.1016/j.padiff.2024.100941","DOIUrl":"10.1016/j.padiff.2024.100941","url":null,"abstract":"<div><div>Magnetized hybrid nanofluid combined with ferrite and silver in a blood-based liquid presents their vital role in several aspects such as artificial heart pumping system, drug delivery process, the flow of blood in the artery, etc. This is because the high heat transportation rate of the nanofluid is caused by the inclusion of nanoparticles. The current investigation is based on the characteristic of particle concentration comprised of Fe<sub>3</sub>O<sub>4</sub> and Ag in the base liquid blood that passed in between two infinite parallel disks filled with porous matrix. The electrically conducting fluid associated to maximum of 1.5 % of volume concentration from each of the solid particles affects the flow phenomena. However, the impact of thermal radiation vis-à-vis the heat dissipation provides efficient heat transport properties with the inclusion of the effective thermal conductivity assumed from the Hamilton-Crosser model. The proposed conductivity model describes the role of particle shapes on the enhanced thermal properties. Further, numerical treatment is obtained for the transformed designed problem following similarity rules that are used for the conversion of the governing equations into their non-dimensional form. The computation of various flow profiles leads to get the entropy generation due to the irreversibility processes. Along with the fluid velocity and temperature distributions, the study is carried out for the entropy as well as the computation of Bejan number and afterwards the simulation of the shear and heat transportation rate are also depicted graphically. The main finding of the proposed study is that solid particle concentrations have a substantial impact to increasing fluid velocity in magnitude, resulting in a narrower wall thickness at both channel walls. Thermal radiation was shown to be more effective at increasing entropy generation and Bejan value.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical illustration using finite difference method for the transient flow through porous microchannel and statistical interpretation of entropy using response surface methodology","authors":"","doi":"10.1016/j.padiff.2024.100940","DOIUrl":"10.1016/j.padiff.2024.100940","url":null,"abstract":"<div><div>The current article discloses the influence of the hyperbolic tangent nanofluid on time dependent flow through a microchannel when a magnetic field is applied. The porous medium was incorporated using the Darcy–Forchheimer model. The chemical reaction is explained by Arrhenius activation energy. Temperature is determined by convective boundary conditions. The irreversibility occurring in the flow is analyzed. The modeled problem gives rise to partial differential equations, which are computed by finite difference method. Response surface methodology, an optimization technique, is used to attain the optimal conditions for entropy generated for the flow of fluid. Results of the analysis reveal that concentration decreases with the rise in reaction rate parameter and increases with activation energy parameter. Prandtl and Eckert numbers, with their increase, enhance entropy, and fluid friction irreversibility is at its highest. Perfect co-relation is attained for the model by the response surface methodology, with a co-relation coefficient of 100 %. The Weissenberg number is highly sensitive to change in the present modeling, followed by Darcy and Reynolds numbers. The Reynolds number and Darcy number show positive sensitivity, while the Weissenberg number shows negative sensitivity to the entropy generated.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method","authors":"","doi":"10.1016/j.padiff.2024.100937","DOIUrl":"10.1016/j.padiff.2024.100937","url":null,"abstract":"<div><div>In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computational analysis of radiative flow of power law fluid with heat generation effects: Galerkin finite element simulations","authors":"","doi":"10.1016/j.padiff.2024.100927","DOIUrl":"10.1016/j.padiff.2024.100927","url":null,"abstract":"<div><div>This research aims to presents the free convective flow power law fluid due to vertical cone. The investigation for observing the heat transfer phenomenon is accounted to heat generation and radiative effects. The assumption of variable viscosity is taken into account. A vertical cone induced the flow. The dimensionless variables are followed to attains the simplified form. The numerical computations are performed with help of famous finite element method (FEM). The FEM algorithm is supported with applications of quadratic Lagrange polynomials. The results are confirmed with peak accuracy. The physical aspect of problem is presented in view of shear thickening, shear thinning and viscous material case. A comparative thermal reflection in absence and presence of heat generation have been endorsed. Moreover, the insight of various parameters on Nusselt number is also presented.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}