A novel formulation of the fuzzy hybrid transform for dealing nonlinear partial differential equations via fuzzy fractional derivative involving general order

Abstract

<abstract><p>The main objective of the investigation is to broaden the description of Caputo fractional derivatives (in short, CFDs) (of order $ 0 < \alpha < r $) considering all relevant permutations of entities involving $ t_{1} $ equal to $ 1 $ and $ t_{2} $ (the others) equal to $ 2 $ via fuzzifications. Under $ {g\mathcal{H}} $-differentiability, we also construct fuzzy Elzaki transforms for CFDs for the generic fractional order $ \alpha\in(r-1, r) $. Furthermore, a novel decomposition method for obtaining the solutions to nonlinear fuzzy fractional partial differential equations (PDEs) via the fuzzy Elzaki transform is constructed. The aforesaid scheme is a novel correlation of the fuzzy Elzaki transform and the Adomian decomposition method. In terms of CFD, several new results for the general fractional order are obtained via $ g\mathcal{H} $-differentiability. By considering the triangular fuzzy numbers of a nonlinear fuzzy fractional PDE, the correctness and capabilities of the proposed algorithm are demonstrated. In the domain of fractional sense, the schematic representation and tabulated outcomes indicate that the algorithm technique is precise and straightforward. Subsequently, future directions and concluding remarks are acted upon with the most focused use of references.</p></abstract>

Endpoint Estimates for Commutators of Fractional Integral Operators on the p-Adic Vector Space

“…Moreover, it is applied in the solution of linear constant coefficient fractional differential equations of any commensurate order and the CRONE control-system design tool-box for the control engineering community (see [19,20] and related references therein). Recently many researchers have made tremendous contributions to the topic of fractional calculus by developing multiple fractional expressions in diverse publications (see, for instance, [4,25,26,28,[30][31][32]). Also, its applications have been found in various fields of science and engineering, such as rheology, fluid flow, probability, and electrical networks.…”

Estimates for p-adic fractional integral operator and its commutators on p-adic Morrey–Herz spaces

“…Moreover, it is applied in the solution of linear constant coefficient fractional differential equations of any commensurate order and the CRONE control-system design toolbox for the control engineering community (see [17,18] and related references therein). Recently many researchers have made tremendous contributions to the topic of fractional calculus by developing multiple fractional expressions in diverse publications (see, for instance, [19][20][21][22][23][24][25]). Also, its applications have been found in various fields of science and engineering, such as rheology, fluid flow, probability, and electrical networks.…”