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New approach on the solutions of nonlinear q-hybrid integro-differential equations

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Abstract

The momentous objective in this paper is to prove existence as well as approximations of solution in hybrid initial value problem with fractional q-derivative in Caputo sense. The main approach is based on the operator theoretic technique in a partially ordered metric space. The results are obtained under weaker partially conditions and partially Lipschitz conditions via Dhage iteration method. Examples illustrating the results are also presented.

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Authors and Affiliations

  1. Department of Mathematics, Neka Branch, Islamic Azad University, Neka, 48411/86114, Iran

    Rahmat Darzi

  2. Department of mathematics, Central Tehran Branch Islamic Azad university, Tehran, 13185/768, Iran

    Meysam Alvan & Amin Mahmoodi

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  1. Rahmat Darzi
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  2. Meysam Alvan
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  3. Amin Mahmoodi
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Darzi, R., Alvan, M. & Mahmoodi, A. New approach on the solutions of nonlinear q-hybrid integro-differential equations. Anal.Math.Phys. 11, 19 (2021). https://doi.org/10.1007/s13324-020-00465-1

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  • DOI: https://doi.org/10.1007/s13324-020-00465-1

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