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2023 | OriginalPaper | Chapter

On the Existence and Stability Analysis for \(\varPsi \)-Caputo Fractional Boundary Value Poblem

Authors : Bhagwat R. Yewale, Deepak B. Pachpatte

Published in: Frontiers in Industrial and Applied Mathematics

Publisher: Springer Nature Singapore

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Abstract

The chapter focuses on the qualitative analysis of fractional boundary value problems involving -Caputo fractional derivatives. It begins by introducing the concept of fractional calculus and its relevance in modeling physical phenomena. The main contributions include the proof of existence and uniqueness of solutions using Banach fixed point theorem and a thorough stability analysis involving Ulam-Hyers, Generalized Ulam-Hyers, Ulam-Hyers-Rassias, and Generalized Ulam-Hyers-Rassias stability. The chapter also includes an illustrative example to demonstrate the theoretical results, highlighting the practical applicability of the study. The work is particularly notable for its rigorous mathematical treatment and the general nature of the results, which can be extended to various classical fractional operators.

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Title: On the Existence and Stability Analysis for -Caputo Fractional Boundary Value Poblem
Authors: Bhagwat R. Yewale
Deepak B. Pachpatte
Publisher: Springer Nature Singapore
Book: Frontiers in Industrial and Applied Mathematics
Print ISBN: 978-981-19-7271-3

Electronic ISBN: 978-981-19-7272-0

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-981-19-7272-0_18

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