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A validation on concept of formula for variable order integral and derivatives

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  • Chauhan, Archana
  • Gautam, G.R.
  • Chauhan, S.P.S.
  • Dwivedi, Arpit

Abstract

This paper deals and addresses the query that which of the variable order operators are reasonable and regular extension of constant order operators. An irregularity is pointed out in the definition of variable order operators. We generalize some existing results of constant order to variable order using special functions of fractional calculus. It provides a method for considering the existence of solution for variable order fractional differential equations. Some illustrations are presented to support the validity of variable order operators. Further, we consider an application of a class of fractional initial value problems and provide the criteria of existence and uniqueness of its solution with example.

Suggested Citation

  • Chauhan, Archana & Gautam, G.R. & Chauhan, S.P.S. & Dwivedi, Arpit, 2023. "A validation on concept of formula for variable order integral and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001984
    DOI: 10.1016/j.chaos.2023.113297
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    References listed on IDEAS

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    1. Zhang, Shuqin & Su, Xinwei, 2021. "Unique existence of solution to initial value problem for fractional differential equation involving with fractional derivative of variable order," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    3. Jiang, Jingfei & Chen, Huatao & Guirao, Juan L.G. & Cao, Dengqing, 2019. "Existence of the solution and stability for a class of variable fractional order differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 269-274.
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