Fuzzy linear singular differential equations under granular differentiability concept

Najariyan, Marzieh; Pariz, Naser; Vu, Ho

doi:10.1016/j.fss.2021.01.003

Cited by 24 publications

(5 citation statements)

References 21 publications

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“…Mazandarani and Li [22] presented a review on FDEs. Najariyan et al [23,24] investigated the solution of singular FDEs with the concept of gr-differentiability. Soma et al [25,26] established conditions for the existence and uniqueness of solutions for fuzzy initial value problems and system of fuzzy boundary value problems under gr-differentiability.…”

Section: Articlementioning

confidence: 99%

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Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability

Soma,

Suresh Kumar,

Agarwal

et al. 2023

Fuzzy Information and Engineering

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This paper considers fuzzy boundary value problems associated with second-order fuzzy differential equations under granular differentiability. Using a horizontal membership function, we present the notion of second-order granular differentiability for fuzzy functions. Using the granular differentiability concept, we interpret two kinds of two-point boundary value problems for second-order fuzzy differential equations. Sufficient conditions are established for the existence and uniqueness of solutions to these fuzzy boundary value problems. An algorithm is presented for solving non-linear fuzzy boundary value problems under granular differentiability. We provide one example and two engineering applications to demonstrate the algorithm's effectiveness and results.

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Section: Articlementioning

confidence: 99%

“…Theorem 1.3 [23] Let be an FF, then is twice gr-differentiable if and only if its HMF is twice differentiable with respect to . Moreover,…”

Section: Articlementioning

confidence: 99%

Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability

Soma,

Suresh Kumar,

Agarwal

et al. 2023

Fuzzy Information and Engineering

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“…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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“…Mazandarani et al [9] established granular differentiability (gr-differentiability), a novel idea of FF differentiability based on RDM-IA and horizontal membership functions (HMF). Najariyan et al [12] investigated the solution of singular FDEs with the concept of gr-differentiability. Under the concept of gr-differentiability, Najariyan et al [11] effectively tune the fuzzy granular PID controller using a particle swarm optimization algorithm.…”

Section: Introductionmentioning

confidence: 99%

Solution for a System of First-Order Linear Fuzzy Boundary Value Problems

Nagalakshmi¹,

Kumar²,

Madhavi³

2023

Int. J. Anal. Appl.

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In this paper, we consider homogeneous and non-homogeneous system of first order linear fuzzy boundary value problems (SFOLBVPs) under granular differentiability. Using the concept of horizontal membership function, we introduced the notion of first order granular differentiability for n-dimensional fuzzy functions. We present granular integral and its properties. Theorems on the existence and uniqueness of solutions for homogeneous and non-homogeneous SFOLFBVPs are proved. We develop an algorithm for solution of non-homogeneous SFOLBVPs under granular differentiability. We provide some examples to illustrate the validity of the proposed algorithm.

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Fuzzy linear singular differential equations under granular differentiability concept

Cited by 24 publications

References 21 publications

Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability

Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability

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

Solution for a System of First-Order Linear Fuzzy Boundary Value Problems

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