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Fractional Derivatives with Variable Memory

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Abstract

Recently, fractional derivatives (FDs) and fractional differential equations are extensively used in modeling of most dynamic processes which generally involve memory factors. Normally, the dynamic models involving full memory effect can be solved with the help of global fractional derivatives, whereas those involves with local memory effect can be solved by using only fractional derivatives with short memory. The prime objective of this work is to define new fractional derivatives of Riemann–Liouville and Caputo types, which can be used for both short and global memory effects. Some general and dynamic properties of the proposed differential operators in comparison to existing formulas of FDs are discussed.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable suggestions that improved this paper remarkably. Present work is partially supported by NBHM, DAE, Mumbai, under the Grant No. 02011/7/2020/NBHM(RP)/R&D/6289.

Funding

Present submission is partially supported with NBHM, DAE, Mumbai, under the Grant No. 02011/7/2020/NBHM(RP)/R&D/6289.

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Authors and Affiliations

  1. Institute of Mathematics and Applications, Bhubaneswar, Odisha, 751029, India

    P. Baliarsingh

  2. Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology, Bhubaneswar, 751024, India

    L. Nayak

Authors
  1. P. Baliarsingh
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  2. L. Nayak
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Both the authors have contributed equally for preparing this submission.

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Correspondence to L. Nayak.

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We have no conflicts of interest in- cluding any financial, personal or other relationships with other people or organiza- tions to disclose.

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Baliarsingh, P., Nayak, L. Fractional Derivatives with Variable Memory. Iran J Sci Technol Trans Sci 46, 849–857 (2022). https://doi.org/10.1007/s40995-022-01296-4

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  • DOI: https://doi.org/10.1007/s40995-022-01296-4

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