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In this paper, a new method is proposed to solve type‐2 fuzzy linear system of equations by converting the system into three interval linear systems and one crisp linear system of equations. In this work, three possible cases of type‐2 fuzzy linear system is considered depending upon uncertainty (as type‐2 fuzzy number) in right‐hand side vector B˜$$ \tilde{B} $$, in co‐efficient matrix A˜$$ \tilde{A} $$, and both in co‐efficient matrix A˜$$ \tilde{A} $$ as well as right‐hand side vector B˜$$ \tilde{B} $$. Triangular perfect quasi type‐2 fuzzy numbers are taken to propose the new method. The main significance of the proposed method is that it uses the arithmetic of interval theory, which makes this method easier to handle. Five numerical examples are solved to show the validation of the proposed technique. Further, two application problems related to 6‐bar truss and rectangular sheet are encountered in type‐2 fuzzy environment. Comparison among the results obtained by the present method and previously achieved results is also made in this work, which shows that the results are close enough and, in some cases, better bounds for the solution are obtained. [ABSTRACT FROM AUTHOR]

The analysis of interpersonal relationships has started to become popular in the last few decades. Interpersonal relationships exist in many ways, including family, friendship, job, and clubs. In this manuscript, we have implemented the homotopy perturbation Elzaki transform method to obtain the solutions of romantic and interpersonal relationships model involving time‐fractional‐order derivatives with non‐singular kernels. The present method is the combination of the classical homotopy perturbation method and the Elzaki transform. This method offers a rapidly convergent series of solutions. The present approach explores the dynamics of love between couples. Validation and usefulness of the method are incorporated with new fractional‐order derivatives with exponential decay law and with general Mittag–Leffler law. Obtained results are compared with the established solution defined in the Caputo sense. Further, a comparative study among Caputo and newly defined fractional derivatives are discussed. [ABSTRACT FROM AUTHOR]

A widescale description of various phenomena in science and engineering such as physics, chemical, acoustics, control theory, finance, economics, mechanical engineering, civil engineering, and social sciences is well described by nonlinear fractional differential equations (NLFDEs). In turbulence, fluid dynamics, and nonlinear biological systems, applications of NLFDEs can also be found. NLFDEs are believed to be powerful tools to describe real‐world problems more precisely than the differential equation of the integer‐order. In this research, we have used the fractional reduced differential transform method (FRDTM) to find the solution of the time‐fractional Sawada‐Kotera‐Ito seventh‐order equation. The novelty of the FRDTM is that it does not require any discretization, transformation, perturbation, or any restrictive conditions. In addition, compared to other methods, this approach needs less calculation. For special cases of an integer and noninteger orders, computed results are compared with existing results. Present results are in good agreement with the existing solutions. Here, the fractional derivatives are considered in the Caputo sense. Convergence analysis of the results has also been studied with the increasing number of terms of the solution. [ABSTRACT FROM AUTHOR]

In this paper, an interval solution has been constructed for the system of differential equations (SDEs) governing the COVID‐19 pandemic with uncertain parameters, namely, interval. The imposition of lockdown on infective has been considered as an interval parameter. As a result, the complete system of first‐order differential equations is transformed into interval form. The resulting interval system of differential equations (ISDEs) has been solved with help of the parametric concept and the Runge–Kutta method of order 4. Obtained results are compared with existing crisp results, and they are found to be in good agreement. [ABSTRACT FROM AUTHOR]