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Fuzzy fractional framework under granular ψ-Caputo fractional derivative with applications to supply chain dynamics | ||
| Iranian Journal of Fuzzy Systems | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 مهر 1405 اصل مقاله (803.88 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.54397.9638 | ||
| نویسندگان | ||
| Ghulam Muhammad1؛ Qingyu Zhang* 1؛ Muhammad Akram2؛ Tofigh Allahviranloo3 | ||
| 1Research Institute of Business Analytics and SCM, College of Management, Shenzhen University, Shenzhen, China | ||
| 2Institute of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan | ||
| 3Research Center of Performance and Productivity Analysis, Istinye University, Istanbul, Turkey | ||
| چکیده | ||
| This article develops a mathematical framework for fuzzy fractional differential system using the concept of granular Caputo fractional derivative with respect to another function ψ within the horizontal membership function (HMF)-based granular differentiability framework. The propose technique addresses the need for a unified approach that simultaneously incorporate the function ψ as memory kernels for flexible modeling, multi-dimensional representation of uncertainty through HMFs, and analytical fuzzy solution using granular fuzzy Laplace transform with respect to another function (LTWR-AF). First, we introduce the granular ψ-fuzzy fractional integral (ψ-FFI), granular ψ-Caputo fractional derivative (ψ-CFD) and granular fuzzy LTWR-AF. Fundamental properties, results, and relationships among these properties are established in HMF representation. Based on this foundation, closed-form analytical fuzzy solution (AFS) of granular Caputo fuzzy fractional differential equations (GCFFDEs) involving granular ψ-CFD are determined and expressed compactly in terms of Mittag-Leffler function (M-LF). Moreover, the existence and uniqueness (E&U) of the fuzzy solutions for the abstract granular Caputo fuzzy fractional differential system (GCFFDS) with fuzzy parameters and initial data are examined under mild conditions. To illustrate the applicability of the proposed framework, the proposed methodology is applied to the granular Caputo fuzzy fractional sustainable, impact-intensive, quarantined, and recycled/remanufactured (SIQR) supply-chain model under environmental disruptions. Numerical simulations and graphical representations demonstrate that the proposed model effectively describe the uncertainty propagation and memory-dependent behavior in supply-chain dynamics. | ||
| کلیدواژهها | ||
| Fuzzy fractional calculus؛ granular ψ-Caputo fractional derivative؛ horizontal membership functions؛ existence and uniqueness؛ supply chain resilience | ||
| مراجع | ||
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