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Analysis of Q-Fractional Implicit Differential Equation with Nonlocal Riemann–Liouville and Erdélyi-Kober Q-Fractional Integral Conditions

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Abstract

This manuscript aims to present the existence, uniqueness, and various kinds of Ulam’s stability for the solution of the implicit q-fractional differential equation corresponding to nonlocal Erdélyi-Kober q-fractional integral conditions. We use different fixed point theorems to obtain the existence and uniqueness of solution. For stability, we utilize the classical technique of nonlinear functional analysis. The examples are presented as applications to illustrate the main results.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan

    Akbar Zada, Mehboob Alam, Khansa Hina Khalid & Ramsha Iqbal

  2. Department of Exact Science and Engineering, 1 Decembrie 1918 University of Alba Iulia, Alba Iulia, 510009, Romania

    Ioan-Lucian Popa

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  1. Akbar Zada
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  2. Mehboob Alam
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Correspondence to Mehboob Alam.

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Zada, A., Alam, M., Khalid, K.H. et al. Analysis of Q-Fractional Implicit Differential Equation with Nonlocal Riemann–Liouville and Erdélyi-Kober Q-Fractional Integral Conditions. Qual. Theory Dyn. Syst. 21, 93 (2022). https://doi.org/10.1007/s12346-022-00623-9

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