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Solutions of Second-Order Nonlinear Implicit ψ-Conformable Fractional Integro-Differential Equations with Nonlocal Fractional Integral Boundary Conditions in Banach Algebra
by
Yahia Awad
Yahia Awad 1,*
and
Yousuf Alkhezi
Yousuf Alkhezi 2
1
Department of Mathematics and Physics, Lebanese International University (LIU), Bekaa Campus, Al-Khyara P.O. Box 5, West Bekaa, Lebanon
2
Mathematics Department, College of Basic Education, Public Authority for Applied Education and Training (PAAET), P.O. Box 34053, Kuwait City 70654, Kuwait
*
Author to whom correspondence should be addressed.
Symmetry 2024, 16(9), 1097; https://doi.org/10.3390/sym16091097 (registering DOI)
Submission received: 22 June 2024
/
Revised: 11 August 2024
/
Accepted: 15 August 2024
/
Published: 23 August 2024
Abstract
In this paper, we introduce and thoroughly examine new generalized -conformable fractional integral and derivative operators associated with the auxiliary function . We rigorously analyze and confirm the essential properties of these operators, including their semigroup behavior, linearity, boundedness, and specific symmetry characteristics, particularly their invariance under time reversal. These operators not only encompass the well-established Riemann–Liouville and Hadamard operators but also extend their applicability. Our primary focus is on addressing complex fractional boundary value problems, specifically second-order nonlinear implicit -conformable fractional integro-differential equations with nonlocal fractional integral boundary conditions within Banach algebra. We assess the effectiveness of these operators in solving such problems and investigate the existence, uniqueness, and Ulam–Hyers stability of their solutions. A numerical example is presented to demonstrate the theoretical advancements and practical implications of our approach. Through this work, we aim to contribute to the development of fractional calculus methodologies and their applications.
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MDPI and ACS Style
Awad, Y.; Alkhezi, Y.
Solutions of Second-Order Nonlinear Implicit ψ-Conformable Fractional Integro-Differential Equations with Nonlocal Fractional Integral Boundary Conditions in Banach Algebra. Symmetry 2024, 16, 1097.
https://doi.org/10.3390/sym16091097
AMA Style
Awad Y, Alkhezi Y.
Solutions of Second-Order Nonlinear Implicit ψ-Conformable Fractional Integro-Differential Equations with Nonlocal Fractional Integral Boundary Conditions in Banach Algebra. Symmetry. 2024; 16(9):1097.
https://doi.org/10.3390/sym16091097
Chicago/Turabian Style
Awad, Yahia, and Yousuf Alkhezi.
2024. "Solutions of Second-Order Nonlinear Implicit ψ-Conformable Fractional Integro-Differential Equations with Nonlocal Fractional Integral Boundary Conditions in Banach Algebra" Symmetry 16, no. 9: 1097.
https://doi.org/10.3390/sym16091097
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