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Analysis of incommensurate multi-order fuzzy fractional differential equations under strongly generalized fuzzy Caputo’s differentiability

Granular Computing (2022)Cite this article

Abstract

Analytical studies of fuzzy fractional differential equations (FFDEs) of two different independent fractional orders are often complex and difficult. It is essential to develop comprehensive schemes for the solutions of FFDEs with independent orders. This article introduces and investigates the fully closed-form analytical solutions of FFDEs involving two different independent fractional orders under the strongly generalized Hukuhara differentiability (SGHD). Based on the concept of SGHD, we extract two possible solutions of FFDEs in terms of the Mittag-Leffler function. Potential solutions for homogeneous and inhomogeneous FFDEs are obtained using the definition of the fuzzy Laplace transform technique. Some interesting properties and results for the FFDEs are introduced using the concepts of SGHD. We illustrate some examples as applications to explain the effectiveness of our proposed results. FFDE has a variety of applications in science and engineering. To enhance the functional significance of this work, we solve the RLC circuit using the proposed technique in a fuzzy setting to analyze and interpret the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram

  2. Department of Mathematics, Lahore Garrison University, Lahore, 54000, Pakistan

    Ghulam Muhammad

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  1. Muhammad Akram
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  2. Ghulam Muhammad
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Correspondence to Muhammad Akram.

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Akram, M., Muhammad, G. Analysis of incommensurate multi-order fuzzy fractional differential equations under strongly generalized fuzzy Caputo’s differentiability. Granul. Comput. (2022). https://doi.org/10.1007/s41066-022-00353-y

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Keywords

  • Fuzzy differential equations with independent fractional orders
  • Caputo fractional derivative
  • Strongly generalized Hukuhara differentiability
  • Laplace transform
  • Mittag-Leffler function