Fuzzy solution of system of fuzzy fractional problems using a reliable method

Haq, Ehsan Ul; Hassan, Qazi Mahmood Ul; Ahmad, Jamshad; Ehsan, Kubra

doi:10.1016/j.aej.2021.08.034

Cited by 15 publications

(6 citation statements)

References 33 publications

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“…He [ 24 ] originally demonstrated that Variational Iteration Method (VIM) is the most complete, streamlined, and user-friendly approach to solving differential equations. Its use for dealing with highly non-linear phenomena has been widely explored by scholars.…”

Section: Analytical Proceduresmentioning

confidence: 99%

“…Its use for dealing with highly non-linear phenomena has been widely explored by scholars. For approximate solutions of non-linear differential equations, he [ 24 ] applied this method. Employing a Lagrange Multiplier, the VIM lowers the need for extensive computational work and sequential integration while keeping a high degree of accuracy.…”

Section: Analytical Proceduresmentioning

confidence: 99%

“…Pervaiz et al [ 23 ] apply Homotopy analysis to approximate a response to the basic HIV viral dynamic framework that describes viral dynamics in vulnerable hosts. Ehsan et al [ 24 ] presented the fractional differential transform method (FDTM) to find the analytical fuzzy solution of various fuzzy fractional differential equations in Caputo sense, which are used to study many physical models in many sciences and engineering domains.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

Shoaib¹,

Shah²,

Nisar³

et al. 2023

Heliyon

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Section: Analytical Proceduresmentioning

confidence: 99%

Section: Analytical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

Shoaib¹,

Shah²,

Nisar³

et al. 2023

Heliyon

View full text Add to dashboard Cite

“…The application of noninteger calculus concepts to uncertain environments, where the system's parameters are represented by uncertain numbers rather than precisely defined, has recently garnered increasing interest. Uncertain fractional calculus was developed as a result, and it has yielded promising outcomes when modeling and analyzing complex systems under uncertainty [7][8][9]. Herein, we will explore the concept of ambiguous fractional calculus and its connection to UM-FDPs.…”

Section: Introduction and Contentsmentioning

confidence: 99%

Uncertain M-fractional differential problems: existence, uniqueness, and approximations using Hilbert reproducing technique provisioner with the case application: series resistor-inductor circuit

Maayah,

Arqub

2024

Phys. Scr.

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In this article, the principle of characterization is proposed as a new tool for solving uncertain M-fractional differential problems under firmly generalized differentiability. The study demonstrates the solvability of such issues by presenting theoretical implications on the existence and uniqueness of two uncertain M-solutions. Additionally, the study provides quantitative solutions in a novel uncertain framework using two Hilbert spaces that are combined through the kernel-based Gram-Schmidt orthogonalization technique. The proposed uncertain problems and algorithms are examined, with a focus on analyzing the solution collection, assessing convergence, and evaluating errors. The debatable Hilbert approach can solve numerous M-fractional differential problems under uncertainty, and the numerical results demonstrate the accuracy and effectiveness of the algorithm. Based on the figures, tables, and quantitative analysis, our work significantly enhances mathematical tools for solving complex M-fractional differential problems under uncertainty. By utilizing the numerical pseudocode; this advancement has the potential to make an impact on various scientific and engineering fields. The final section presents numerical notes, along with recommendations for future research directions. Additionally, an evaluation of the study's findings is provided based on the conducted analysis.

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“…In recent years, several researchers and scientists have concentrated on the theoretical aspects of fuzzy issues such as Modelling population models, assessing civil engineering and weapon systems, and modelling electrodynamics. Some of its applications have been discussed in many real-life scenarios, such as medicine [10], components of the golden means [11] and practical schemes [12]. There are several research on precognition fuzzy and their application in fuzzy controls [13], Ralescu [14], Dubois and Prade [15], Allahviranloo [16], and Verma and Meher [17].…”

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.

show abstract

Fuzzy solution of system of fuzzy fractional problems using a reliable method

Cited by 15 publications

References 33 publications

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

Uncertain M-fractional differential problems: existence, uniqueness, and approximations using Hilbert reproducing technique provisioner with the case application: series resistor-inductor circuit

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

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