Abstract
This article investigates the semi-analytical method coupled with a new hybrid fuzzy integral transform and the Adomian decomposition method via the notion of fuzziness known as the Elzaki Adomian decomposition method (briefly, EADM). In addition, we apply this method to the time-fractional Swift–Hohenberg equation (SHe) with various initial conditions (IC) under gH-differentiability. Some aspects of the fuzzy Caputo fractional derivative (CFD) with the Elzaki transform are presented. Moreover, we established the general formulation and approximate findings by testing examples in series form of the models under investigation with success. With the aid of the projected method, we establish the approximate analytical results of SHe with graphical representations of initial value problems by inserting the uncertainty parameter 0≤℘≤1 with different fractional orders. It is expected that fuzzy EADM will be powerful and accurate in configuring numerical solutions to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.
Highlights
Fractional calculus (FC) is widely regarded as an essential method for characterizing real-world scenarios
FC research includes a number of modifications in consideration of fractional operator nonlocal qualities, increased level of autonomy, and optimum informational implementation, and these characteristics exclusively manifest in fractional order procedures, not integer-order processes
The objective of the current study is to develop a reliable approach for obtaining approximated findings for fuzzy fractional Swift–Hohenberg equation (SHe), the generic SHe containing diffraction components susceptible to ambiguity in initial conditions due to EADM, which simulates the evolution behaviour under consideration
Summary
Fractional calculus (FC) is widely regarded as an essential method for characterizing real-world scenarios. Whereas mathematicians consider FC to be an essential resource in scientific research, the subject of fractional operators’ existence is invariably addressed in several domains. Specialists have created fractional differential equations (FDEs) to analyse and comprehend scientific developments in a multitude of disciplines. FC research includes a number of modifications in consideration of fractional operator nonlocal qualities, increased level of autonomy, and optimum informational implementation, and these characteristics exclusively manifest in fractional order procedures, not integer-order processes. The concept of partial differential equations (PDEs) has become increasingly important in modelling scientific and mechanical challenges including thermodynamics, electrostatistics, solid state physics, and biological sciences. Instead of using crisp values, parameters, and predictor variables, one can employ uncertainty contexts to combat ambiguity and subtlety. Generic PDES become fuzzy PDEs as a result of this uncertainty.
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