Hyers-Ulam Stability and Existence Criteria for the Solution of Second-Order Fuzzy Differential Equations

Jamal, Noor; Sarwar, Muhammad; Khashan, M. Motawi

doi:10.1155/2021/6664619

Cited by 3 publications

(2 citation statements)

References 24 publications

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“…To conduct a comprehensive stability analysis of the proposed model, we revisit several definitions [45] . Consider

as a self-map defined by:…”

Section: Stability Criteriamentioning

confidence: 99%

On mathematical modelling of measles disease via collocation approach

Ahmed,

Jahan,

Shah

et al. 2024

AIMSPH

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<abstract> <p>Measles, a highly contagious viral disease, spreads primarily through respiratory droplets and can result in severe complications, often proving fatal, especially in children. In this article, we propose an algorithm to solve a system of fractional nonlinear equations that model the measles disease. We employ a fractional approach by using the Caputo operator and validate the model's by applying the Schauder and Banach fixed-point theory. The fractional derivatives, which constitute an essential part of the model can be treated precisely by using the Broyden and Haar wavelet collocation methods (HWCM). Furthermore, we evaluate the system's stability by implementing the Ulam-Hyers approach. The model takes into account multiple factors that influence virus transmission, and the HWCM offers an effective and precise solution for understanding insights into transmission dynamics through the use of fractional derivatives. We present the graphical results, which offer a comprehensive and invaluable perspective on how various parameters and fractional orders influence the behaviours of these compartments within the model. The study emphasizes the importance of modern techniques in understanding measles outbreaks, suggesting the methodology's applicability to various mathematical models. Simulations conducted by using MATLAB R2022a software demonstrate practical implementation, with the potential for extension to higher degrees with minor modifications. The simulation's findings clearly show the efficiency of the proposed approach and its application to further extend the field of mathematical modelling for infectious illnesses.</p> </abstract>

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“…To conduct a comprehensive stability analysis of the proposed model, we revisit several definitions [45] . Consider

as a self-map defined by:…”

Section: Stability Criteriamentioning

confidence: 99%

On mathematical modelling of measles disease via collocation approach

Ahmed,

Jahan,

Shah

et al. 2024

AIMSPH

View full text Add to dashboard Cite

show abstract

“…For basic concept of natural transform method intrusted readers can see Refs. 21 – 24 . The advection equations and advection-diffusion equations have been solved by the authors of Refs.…”

Section: Introductionmentioning

confidence: 99%

Solutions of fuzzy advection-diffusion and heat equations by natural adomian decomposition method

Jamal,

Sarwar,

Agarwal

et al. 2023

Sci Rep

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In this article, we present an algorithm for computing analytical solutions of linear fuzzy advection-diffusion equations and one-dimensional fuzzy heat equations involving an external source. The fuzzy problems can be solved by using the natural transform and Adomian decomposition method. The results obtained through the natural Adomian decomposition method are calculated in a series form that converges rapidly to the exact solution. To enhance the practicality of our work, we provide examples to illustrate our findings.

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Solution of linear correlated fuzzy differential equations in the linear correlated fuzzy spaces

Jamal,

Sarwar,

Mlaiki

et al. 2023

MATH

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<abstract><p>Linear correlated fuzzy differential equations (LCFDEs) are a valuable approach to handling physical problems, optimizations problems, linear programming problems etc. with uncertainty. But, LCFDEs employed on spaces with symmetric basic fuzzy numbers often exhibit multiple solutions due to the extension process. This abundance of solutions poses challenges in the existing literature's solution methods for LCFDEs. These limitations have led to reduced applicability of LCFDEs in dealing with such types of problems. Therefore, in the current study, we focus on establishing existence and uniqueness results for LCFDEs. Moreover, we will discuss solutions in the canonical form of LCFDEs in the space of symmetric basic fuzzy number which is currently absent in the literature. To enhance the practicality of our work, we provide examples and plots to illustrate our findings.</p></abstract>

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Hyers-Ulam Stability and Existence Criteria for the Solution of Second-Order Fuzzy Differential Equations

Cited by 3 publications

References 24 publications

On mathematical modelling of measles disease via collocation approach

On mathematical modelling of measles disease via collocation approach

Solutions of fuzzy advection-diffusion and heat equations by natural adomian decomposition method

Solution of linear correlated fuzzy differential equations in the linear correlated fuzzy spaces

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