Solution for generalized fuzzy time-fractional Fisher’s equation using a robust fuzzy analytical approach

Verma, Lalchand; Meher, Ramakanta

doi:10.1016/j.joes.2022.03.019

Cited by 15 publications

(7 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the approximate solution and error analysis for both bounds of model 2 are discussed in Table3 Te interval solution on bounds for variable ςϵ[0, 1] when ξ = 4 and η = 0.01 are depicted in Tables 4 and 5. It is observed in Table 1 that absolute errors of the test problem 1 are better in terms of accuracy when compared with existing results given in [48]. Tis shows the strength and validity of the proposed methodology over existing results in the literature.…”

Section: Resultsmentioning

confidence: 55%

“…Te solution to Pythagorean FFDEs was studied under gH-diferentiability in [47]. Furthermore, the q-Homotopy analysis Sumudu transform method (q-HASTM) is utilized to investigate the Fisher equation in [48].…”

Section: Introductionmentioning

confidence: 99%

“…Tis study contains a generalized class of fuzzy-fractional Fisher equations, wherein the initial conditions contain uncertainty. Let us consider the fractional order fuzzy Fisher equation in a general sense as [48]…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New Solutions of Fuzzy‐Fractional Fisher Models via Optimal He–Laplace Algorithm

Qayyum

Tahir

Acharya

2023

International Journal of Intelligent Systems

View full text Add to dashboard Cite

Fuzzy differential equations have gained significant attention in recent years due to their ability to model complex systems in the presence of uncertainty or imprecise information. These equations find applications in various fields, such as biomathematics, horological processes, production inventory models, epidemic models, fluid models, and economic investments. The Fisher model is one such example, which studies the dynamics of a population with uncertain growth rates. This study proposes a dual parametric extension of the He–Laplace algorithm for solving time-fractional fuzzy Fisher models. The proposed methodology uses triangular fuzzy numbers to introduce uncertainty in highly nonlinear fractional differential equations under the generalized Hukuhara differentiability concept. The obtained solutions are validated against existing results in crisp form and are found to be more accurate. The results are analyzed by finding solutions with different values of spatial coordinate ξ , time η , and ς -cut for both upper and lower bounds, and they are presented graphically. The analysis reveals that the uncertain probability density function gradually decreases at left and right boundaries when the fractional order is increased. The study provides valuable insights into the behavior of population growth under uncertain conditions and demonstrates the effectiveness of the proposed methodology in solving fuzzy-fractional models.

show abstract

Section: Resultsmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New Solutions of Fuzzy‐Fractional Fisher Models via Optimal He–Laplace Algorithm

Qayyum

Tahir

Acharya

2023

International Journal of Intelligent Systems

View full text Add to dashboard Cite

show abstract

“…( Ref. 45 ) A fuzzy set is said to be fuzzy number if it is piece-wise continuous, normal (i.e. s.t.…”

Section: Preliminariesmentioning

confidence: 99%

Effect of heat transfer on hybrid nanofluid flow in converging/diverging channel using fuzzy volume fraction

Verma

Meher

Hammouch

et al. 2022

Sci Rep

Self Cite

View full text Add to dashboard Cite

This work explores the magneto-hydrodynamics (MHD) Jeffery–Hamel nanofluid flow between two rigid non-parallel plane walls with heat transfer by employing hybrid nanoparticles, especially Cu and Cu-Al$$_{2}$$ 2 O$$_{3}$$ 3 . Here the MHD nanofluid flow problem is extended with fuzzy volume fraction and heat transfer with diverse nanoparticles to cover the influence of thermal profiles with hybrid nanoparticles on the fuzzy velocity profiles. The nanoparticle volume fraction is described with a triangular fuzzy number ranging from 0 to $$5\%$$ 5 % . A novel double parametric form-based homotopy analysis approach is considered to study the fuzzy velocity and temperature profiles with hybrid nanoparticles in both convergent and divergent channel positions. Finally, the efficiency of the proposed method has been demonstrated by comparing it with the available results in a crisp environment for validation.

show abstract

“…Babakordi et al [38] developed the model of the economy based on the market equilibrium under the fuzzy environment in an ABC sense. Later, Verma and Meher [39] discussed the Fisher and KdV equations in the context of fuzzy time-fractional PDEs under Caputo's gH-differentiability.…”

Section: Introductionmentioning

confidence: 99%

Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

Al-Saedi,

Verma,

Meher

et al. 2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

‎This paper considers a fuzzy nonlinear fifth-order time-fractional Sawada-Kotera equation with a singular kernel and a non-singular Mittag-Leffler kernel‎. ‎The proposed fractional differential equation is discussed with the Caputo and ABC fractional derivative under strongly generalized results and with fuzzy modelling‎. ‎A novel double parametric approach‎, ‎i.e.‎, ‎q-homotopy analysis generalized transform method (q-HAGTM)‎, ‎is considered to find the solution of the proposed model with Caputo and ABC fractional derivatives‎. ‎The problem's uniqueness and convergence analysis are investigated using Banach's fixed point theorem‎. ‎Finally‎, ‎the numerical results have been validated by comparing them with the available results in Caputo and ABC sense under strongly generalized derivatives in the crisp case‎.

show abstract

Solution for generalized fuzzy time-fractional Fisher’s equation using a robust fuzzy analytical approach

Cited by 15 publications

References 31 publications

New Solutions of Fuzzy‐Fractional Fisher Models via Optimal He–Laplace Algorithm

New Solutions of Fuzzy‐Fractional Fisher Models via Optimal He–Laplace Algorithm

Effect of heat transfer on hybrid nanofluid flow in converging/diverging channel using fuzzy volume fraction

Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

Contact Info

Product

Resources

About