Volume 4, Issue 1 (6-2023)                   MACO 2023, 4(1): 97-117 | Back to browse issues page

‎ 10.22034/maco.4.1.9

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Samei M E, Hatami A. To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions. MACO 2023; 4 (1) :97-117
URL: http://maco.lu.ac.ir/article-1-134-en.html
To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions
Mohammad Esmael Samei * , Alireza Hatami
Abstract:   (553 Views)
This paper tries to show that there is only one solution for problem of fractional $q$-differential equations with  Hilfer type, and it does so by using a particular method known as Schaefer's fixed point theorem  and the Banach contraction principle. After that, we create a integral  type of the  problem for nonlocal condition. Next, we show that Ulam stability is true. The Gr"{o}wnwall rule for singular kernels of the equations helps to show our findings are correct. We confirm our findings by giving a few practical examples.
Keywords: implicit $q-$differential equation, Hilfer fractional $q$-derivative, nonlinear analysis, existence, Ulam stability
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Type of Study: Research Article | Subject: Mathematical Analysis
Published: 2024/02/2
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