A study on existence and stability analysis of implicit k,Ψ$$ \left(k,\Psi \right) $$‐Hilfer fractional differential equations and application to RC$$ \mathcal{RC} $$ circuit model

In the present study, we establish the existence and uniqueness of solutions for nonlinear initial value problems and nonlocal boundary value problems associated with implicit fractional differential equations involving ‐Hilfer derivative operator. Furthermore, we explore the stability properties of...

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Bibliographic Details
Published inMathematical methods in the applied sciences
Main Authors Bhupeshwar, Patel, Deepesh Kumar
Format Journal Article
LanguageEnglish
Published 16.10.2024
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Summary:In the present study, we establish the existence and uniqueness of solutions for nonlinear initial value problems and nonlocal boundary value problems associated with implicit fractional differential equations involving ‐Hilfer derivative operator. Furthermore, we explore the stability properties of these solutions in the sense of the Ulam–Hyers, Ulam–Hyers–Rassias, and their generalized stability concepts by proving and applying generalized Gronwall inequality. Lastly, we present the fractional electric circuit model as an example to show the practical applicability of our main results.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10546