To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions

Author(s):

MohammadEsmael Samei* , Alireza Hatami

Message:
Article Type:
Research/Original Article (بدون رتبه معتبر)
Abstract:

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

Language:
English
Published:
Journal of Mathematical Analysis and Convex Optimization, Volume:4 Issue: 1, 2023
Pages:
97 to 117
https://www.magiran.com/p2686802  
سامانه نویسندگان
  • Samei، Mohammad Esmael
    Corresponding Author (1)
    Samei, Mohammad Esmael
    Associate Professor Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran, Bu-Ali Sina University, Hamedan, Iran
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