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In this study, local fuzzy fractional partial differential equations (LFFPDEs) are considered using a hybrid local fuzzy fractional approach. Fractal model behavior can be represented using fuzzy partial differential equations (PDEs) with local fractional derivatives. The current methods are hybrids of the local fuzzy fractional integral transform and the local fuzzy fractional homotopy perturbation method (LFFHPM), the local fuzzy fractional Sumudu decomposition method (LFFSDM) in the sense of local fuzzy fractional derivatives, and the local fuzzy fractional Sumudu variational iteration method (LFFSVIM); these are applied when solving LFFPDEs. The working procedure shows how effective solutions for specific LFFPDEs can be obtained using the applied approaches. Moreover, we present a comparison of the local fuzzy fractional Laplace variational iteration method (LFFLIM), the local fuzzy fractional series expansion method (LFFSEM), the local fuzzy fractional variation iteration method (LFFVIM), and the local fuzzy fractional Adomian decomposition method (LFFADM), which are applied to obtain fuzzy fractional diffusion and wave equations on Cantor sets. To demonstrate the effectiveness of the used techniques, some examples are given. The results demonstrate the major advantages of the approaches, which are equally efficient and simple to use in order to solve fuzzy differential equations with local fractional derivatives. [ABSTRACT FROM AUTHOR]

Activation energy can be elaborated as the minimal energy required to start a certain chemical reaction. The concept of this energy was first presented by Arrhenius in the year 1889 and was later used in the oil reservoir industry, emulsion of water, geothermal as well as chemical engineering and food processing. This study relates to the impacts of mass transfer caused by temperature differences (Soret) and heat transport due to concentration gradient (Dufour) in a Carreau model with nanofluids (NFs), mixed convection and a magnetic field past a stretched sheet. Moreover, thermal radiation and activation energy with new mass flux constraints are presumed. All chemical science specifications of nanofluid are measured as constant. As a result of the motion of nanofluid particles, the fluid temperature and concentration are inspected, with some physical description. A system of coupled partial differential frameworks is used mathematically to formulate the physical model. A numerical scheme named the Runge–Kutta (R-K) approach along with the shooting technique are used to solve the obtained equations to a high degree of accuracy. The MATLAB R2022b software is used for the graphical presentation of the solution. The temperature of the nanofluid encompasses a quicker rate within the efficiency of a Dufour number. An intensifying thermal trend is observed for thermophoresis and the Brownian motion parameter. The Soret effect causes a decline in the fluid concentration, and the opposite trend is observed for rising activation energy. In addition, the local Nusselt number increases with the Prandtl number. Further, the comparative outcomes for drag force are established, with satisfying agreement with the existing literature. The results acquired here are anticipated to be applied to improving heat exchanger thermal efficiency to maintain thermal balancing control in compact heat density equipment and devices. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy variational problem and fuzzy optimal control problem are considered. The granular Euler–Lagrange condition for the fuzzy variational problem and necessary conditions of Pontryagin type for fixed and free final state fuzzy optimal control problem are derived based on the concepts of horizontal membership function (HMF) and granular differentiability with the calculus of variations. Further, based on the proposed solution method, the solutions of fuzzy optimal control problem, i.e., optimal fuzzy control, and corresponding optimal fuzzy state are always fuzzy functions. Finally, the proposed algorithm used to summarize the main steps of solving the fuzzy variational problem and fuzzy optimal control problem numerically using He's variational iteration method (VIM). [ABSTRACT FROM AUTHOR]

In this letter, the differential transform method (DTM) is applied to solve fuzzy fractional wave equation. The elemental properties of this method are investigated based on the two-dimensional differential transform method (DTM), generalized Taylor's formula and fuzzy Coputo's derivative. The proposed method is also illustrated by using some examples. The results reveal that DTM is a highly effective scheme for obtaining analytical solutions of the fuzzy fractional wave equation. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy fractional optimal control problem with both fixed and free final state conditions has been considered. Our problem is defined in the sense of Riemann-Liouville fractional derivative based on Hukuhara difference, and the dynamic constraint is described by a fractional differential equation of order less than 1. Using fuzzy variational approach, a necessary conditions of our problem has been derived. A numerical technique based on Grünwald-Letnikov definition of fractional derivative and the relation between right Riemann-Liouville fractional derivative and right Caputo fractional derivative is proposed. Finally, some numerical examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]