International Journal of Differential Equations
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Acceptance rate13%
Submission to final decision103 days
Acceptance to publication19 days
CiteScore2.600
Journal Citation Indicator0.660
Impact Factor1.6

Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

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International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.

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Research Article

Multiple Solutions for Singular Systems with Sign-Changing Weight, Nonlinear Singularities and Critical Exponent

This paper is an attempt to establish the existence and multiplicity results of nontrivial solutions to singular systems with sign-changing weight, nonlinear singularities, and critical exponent. By using variational methods, the Nehari manifold, and under sufficient conditions on the parameter which represent some physical meanings, we prove some existing results by researching the critical points as the minimizers of the energy functional associated with the proposed problem (2) on the constraint defined by the Nehari manifold, which are solutions of our system, under some sufficient conditions on the parameters , , , and . To the best of our knowledge, this paper is one of the first contributions to the study of singular systems with sign-changing weight, nonlinear singularities, and critical exponent.

Research Article

Stability Results for Nonlinear Implicit -Caputo Fractional Differential Equations with Fractional Integral Boundary Conditions

This article examines the necessary conditions for the unique existence of solutions to nonlinear implicit -Caputo fractional differential equations accompanied by fractional order integral boundary conditions. The analysis draws upon Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Furthermore, the circumstances leading to the attainment of Ulam–Hyers–Rassias forms of stability are established. An illustrative example is provided to demonstrate the derived findings.

Research Article

Solving Nonlinear Fractional PDEs with Applications to Physics and Engineering Using the Laplace Residual Power Series Method

The Laplace residual power series (LRPS) method uses the Caputo fractional derivative definition to solve nonlinear fractional partial differential equations. This technique has been applied successfully to solve equations such as the fractional Kuramoto–Sivashinsky equation (FKSE) and the fractional generalized regularized long wave equation (GRLWE). By transforming the equation into the Laplace domain and replacing fractional derivatives with integer derivatives, the LRPS method can solve the resulting equation using a power series expansion. The resulting solution is accurate and convergent, as demonstrated in this paper by comparing it with other analytical methods. The LRPS approach offers both computational efficiency and solution accuracy, making it an effective technique for solving nonlinear fractional partial differential equations (NFPDEs). The results are presented in the form of graphs for various values of the order of the fractional derivative and time, and the essential objective is to reduce computation effort.

Research Article

Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis

In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model’s stability. By analysing the stability of the model’s uniform equilibrium state, we identify a condition leading to Turing instability. The study delves into how diffusion influences pattern formation within a predator-prey system. Our findings reveal that various spatiotemporal patterns, such as patches, spots, and even chaos, emerge based on species diffusion rates. We derive the amplitude equation by employing the weak nonlinear multiple scales analysis technique and the Taylor series expansion. A novel sinc interpolation approach is introduced. Numerical simulations elucidate the interplay between diffusion and Turing parameters. In a two-dimensional domain, spatial pattern analysis illustrates population density dynamics resulting in isolated groups, spots, stripes, or labyrinthine patterns. Simulation results underscore the method’s effectiveness. The article concludes by discussing the biological implications of these outcomes.

Research Article

Numerical Investigation of MHD Carreau Nanofluid Flow with Nonlinear Thermal Radiation and Joule Heating by Employing Darcy–Forchheimer Effect over a Stretching Porous Medium

Heat transfer in fluid mechanisms has a stronghold in everyday activities. To this end, nanofluids take a leading position in the advent of the betterment of thermal conductivity. The present study examines numerical investigations of incompressible magnetohydrodynamic (MHD) flow of Carreau nanofluid by considering nonlinear thermal radiation, Joule heating, temperature-dependent heat source/sink, and chemical reactions with attached Brownian movement and thermophoresis above a stretching sheet that saturates the porous medium. Pertaining similarity assumptions are used to change the flow equations into tractable forms of higher order nonlinear ordinary differential equations (ODEs). The continuation technique is adopted in the MATLAB bvp4c package for the numerical outcomes. The velocity, temperature, and nanoparticle concentration distributions in contrast to the leading parameters are availed in graphical and tabular descriptions. Among the many outcomes, increasing the radiation parameter from 0.2 to 0.8 surged the heat transfer rate by at n = 1.5 and lifted it only by at n = 0.5. By boosting the magnetic parameter from 0 to 1.5, respective and rises in local drag forces are achieved in shear-thickening and thinning regions. On top of that, chemical reactions and Brownian motion parameters decay the concentration field. The distinctiveness of this method is that a solution is secured for the problem, which is highly sensitive to initial and boundary conditions. It will be worth mentioning that these fluid flow models will be applicable in various fields, such as engineering, petroleum, nuclear safety processes, and medical science.

Research Article

Cost-Effectiveness Analysis of the Optimal Control Strategies for Multidrug-Resistant Tuberculosis Transmission in Ethiopia

Despite the recent progress of global control efforts, tuberculosis (TB) remains a significant public health threat worldwide, especially in developing countries, including Ethiopia. Furthermore, the emergence of multidrug-resistant tuberculosis (MDR-TB) has further complicated the situation. This study aims at identifying the most effective strategies for combating MDR-TB in Ethiopia. We first present a compartmental model of MDR-TB transmission dynamics in Ethiopia. The model is shown to have positive solutions, and the stability of the equilibrium points is analyzed. Then, we extend the model by incorporating time-dependent control variables. These control variables are vaccination, distancing, and treatment for DS-TB and MDR-TB. Finally, the optimality system is numerically simulated by considering different combinations of the strategies, and their cost effectiveness is analysed. Our finding shows that, among single control strategies, the successful treatment of drug-susceptible tuberculosis (DS-TB) is the most effective control factor for eliminating MDR-TB transmission in Ethiopia. Furthermore, within the six dual control strategies, the combination of distancing and successful treatment of DS-TB is less costly and more effective than other strategies. Finally, out of the triple control strategies, the combination of distancing, successful treatment for DS-TB, and treatment for MDR-TB is the most efficient strategy for curbing the MDR-TB disease in Ethiopia. Thus, to reduce MDR-TB efficiently, it is recommended that authorities focus on treating MDR-TB, effective treatment of DS-TB, and promoting social distancing through public health education and awareness programs.

International Journal of Differential Equations
 Journal metrics
See full report
Acceptance rate13%
Submission to final decision103 days
Acceptance to publication19 days
CiteScore2.600
Journal Citation Indicator0.660
Impact Factor1.6
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