A new approach to the fractional Abel k−integral equations and linear fractional differential equations in a fuzzy environment

Van Hoa, Ngo; Allahviranloo, Tofigh; Pedrycz, Witold

doi:10.1016/j.fss.2024.108895

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…Singh et al [28] studied the fuzzy fractional differential equation under generalized Hukuhara difference in a Caputo sense. Van et al [29] discussed the linear fractional differential equation using the Caputo fractional gH-differentiability in a fuzzy environment. Mohapatra and Chakraverty [30] discussed the prey-predator model in a fractional order to solve the Legendre wavelet method in a type-2 fuzzy environment.…”

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.

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‎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.

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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.

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Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations

Truong,

Bohner,

Girejko

et al. 2025

Information Sciences

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Representation of solutions to fuzzy linear fractional differential equations with a piecewise constant argument

Van Phut

2024

Phys. Scr.

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This study marks the first exploration of fuzzy linear fractional differential equations with a piecewise constant argument (FLFDEs-PCA), incorporating the concept of Caputo's type gH-differentiability with the order $\alpha \in (0,1]$. Such problems are noteworthy as they represent hybrid systems, blending the characteristics of continuous and discrete dynamical systems and integrating aspects from both differential and difference equations. The primary objective of this research is to establish a standardized framework for deriving explicit solution formulas for FLFDEs-PCA under various scenarios. Additionally, illustrative examples are provided to demonstrate the practical implications of our theoretical findings.

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A new approach to the fractional Abel k−integral equations and linear fractional differential equations in a fuzzy environment

Cited by 3 publications

References 37 publications

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

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

Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations

Representation of solutions to fuzzy linear fractional differential equations with a piecewise constant argument

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