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Investigation of a class of differential equations of complex order with boundary conditions

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Abstract

In this manuscript, a class of boundary value problems (BVPs) of complex order fractional differential equations (COFDEs) using the Caputo–Fabrizio (C–F) operator is considered. We develop appropriate results for the existence and uniqueness of solution to the problem under our study using Banach and Krasnoselskii’s fixed-point theorem. In addition, some others tools of nonlinear analysis are utilized in the derivation of our results. Additionally, we also derive some necessary conditions for stability analysis of the proposed problem using the concept of Ulam and Hyers (U–H). Finally, an example to justify our theoretical findings is given.

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Acknowledgements

Authors are thankful to Prince Sultan University for support through TAS research lab.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University of Islamabad, Sahiwal Campus, Punjab, Pakistan

    Asma & Anum Mehmood

  2. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia

    Kamal Shah & Thabet Abdeljawad

  3. Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, 18000, Pakistan

    Kamal Shah

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  1. Asma
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  2. Anum Mehmood
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  3. Kamal Shah
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  4. Thabet Abdeljawad
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Correspondence to Kamal Shah or Thabet Abdeljawad.

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Communicated by Dhirendra Bahuguna.

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Asma, Mehmood, A., Shah, K. et al. Investigation of a class of differential equations of complex order with boundary conditions. J Anal (2024). https://doi.org/10.1007/s41478-024-00738-z

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  • DOI: https://doi.org/10.1007/s41478-024-00738-z

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