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Solutions of non-homogeneous system of fuzzy fractional differential equations: a novel approach

  • Fuzzy systems and their mathematics
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Abstract

In this research, a novel approach is applied to obtain the solution for the non-homogeneous system of fuzzy fractional differential equations. The fuzzy fractional initial value problem is split into sets of classical fractional initial value problems. Such a fractional initial value problem is constructed by taking the forcing term derived from each of fuzzy set and the initial value obtained from each of fuzzy intervals. The solution to the fuzzy fractional initial value problem is defined as the collection of all solutions of the classical fractional initial value problems, and its degree of membership is the smallest value among the degrees of membership obtained from forcing terms and initial values in the associated fuzzy sets. Specifically, a solution is constructed as a fuzzy collection of real vector functions, instead of a vector of fuzzy-valued functions. The numerical example has been used to illustrate the proposed approach in detail. The benefits of the proposed methodology over the existing methodology, as well as its applicability to the real world, are clearly demonstrated.

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Authors and Affiliations

  1. Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India

    V. Padmapriya & M. Kaliyappan

  2. New Prince Shri Bhavani Arts and Science College, Chennai, India

    V. Padmapriya

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  1. V. Padmapriya
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  2. M. Kaliyappan
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Correspondence to M. Kaliyappan.

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Padmapriya, V., Kaliyappan, M. Solutions of non-homogeneous system of fuzzy fractional differential equations: a novel approach. Soft Comput 27, 14553–14569 (2023). https://doi.org/10.1007/s00500-023-08956-6

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