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Generalization of Taylor’s formula and differential transform method for composite fractional q-derivative

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Abstract

In the present paper, we first establish a generalized q-Taylor’s formula involving composite fractional q-derivative. Next, we define the generalized q-differential transform and its inverse for composite fractional q-derivative and establish some basic properties for this transform. We also illustrate the effectiveness of these results by solving two fractional q-difference equations.

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Acknowledgements

The support provided through UGC-Minor Research Project under XII plan grant of Maulana Azad National Urdu University, Hyderabad is gratefully acknowledged. The authors are grateful to Prof. Mridula Garg for inspiring discussions and helpful comments during the preparation of the paper. The authors are also thankful to the anonymous referee for the fruitful suggestions which led to the present form of paper.

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Authors and Affiliations

  1. Department of Science and Humanities, Govt. R. C. Khaitan Polytechnic College, Jaipur, 302004, Rajasthan, India

    Lata Chanchlani

  2. Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, 500032, Telangana, India

    Subhash Alha

  3. Department of Mathematics, J. K. Lakshmipat University, Jaipur, 302026, Rajasthan, India

    Jaya Gupta

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  1. Lata Chanchlani
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  2. Subhash Alha
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  3. Jaya Gupta
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Correspondence to Jaya Gupta.

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Chanchlani, L., Alha, S. & Gupta, J. Generalization of Taylor’s formula and differential transform method for composite fractional q-derivative. Ramanujan J 48, 21–32 (2019). https://doi.org/10.1007/s11139-018-9997-7

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  • DOI: https://doi.org/10.1007/s11139-018-9997-7

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