Existence Results for <strong>ψ</strong>-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions

Karthikeyan Panjaiyan; Manikandan Ambigapathi

doi:doi:10.11648/j.iotcc.20261505.14

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Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions

Karthikeyan Panjaiyan^*, Manikandan Ambigapathi

Published in Applied and Computational Mathematics (Volume 15, Issue 5)

Received: 28 May 2026 Accepted: 27 June 2026 Published: 13 October 2026

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Abstract

In this paper, we discuss the existence and uniqueness of solutions for nonlinear fractional integro-differential equations with the ψ-Caputo fractional derivative under slit-strip integral boundary conditions. Fractional differential equations have been the focus of intense interest, since they can express memory and hereditary properties of various materials and processes in science and engineering. The ψ-Caputo fractional derivative which extends some known fractional operators is a very fruitful instrument for modeling multidimensional dynamical systems and thus applicable to a wide variety of problems. The everything aim of current paper is to get certain sufficient conditions that ensures the multi- solvability as well as uniqueness of the boundary value problem. The study is conducted on the pre-determined space which is a Banach space by using nonlinear functional analysis. In particular, suitable estimates for the nonlinearities involved in the equation are obtained by Hölders inequality and the Mönch fixed-point theorem is the main tool for proving existence of solution. In addition, further conditions are required for ensuring the uniqueness of the obtained solution. The present work contributes to the theory of fractional integro-differential equations with nonlocal boundary conditions and generalizes and improves many results in the literature. The addition of slit-strip integral boundary conditions and the ψ-Caputo fractional derivative results in a more generalized- setting for the study of such types of problems. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the theoretical results and to check the correctness of the theoretical results.

Published in	Applied and Computational Mathematics (Volume 15, Issue 5)
DOI	10.11648/j.iotcc.20261505.14
Page(s)	185-197
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Fractional Differential Equations, ψ-Caputo Fractional Derivative, Fractional ψ-integral, Boundary Value Problem, Monch's Fixed Point Theorem

References

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APA Style

Panjaiyan, K., Ambigapathi, M. (2026). Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions. Applied and Computational Mathematics, 15(5), 185-197. https://doi.org/10.11648/j.iotcc.20261505.14

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ACS Style

Panjaiyan, K.; Ambigapathi, M. Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions. Appl. Comput. Math. 2026, 15(5), 185-197. doi: 10.11648/j.iotcc.20261505.14

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AMA Style

Panjaiyan K, Ambigapathi M. Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions. Appl Comput Math. 2026;15(5):185-197. doi: 10.11648/j.iotcc.20261505.14

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@article{10.11648/j.iotcc.20261505.14,
  author = {Karthikeyan Panjaiyan and Manikandan Ambigapathi},
  title = {Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions},
  journal = {Applied and Computational Mathematics},
  volume = {15},
  number = {5},
  pages = {185-197},
  doi = {10.11648/j.iotcc.20261505.14},
  url = {https://doi.org/10.11648/j.iotcc.20261505.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.iotcc.20261505.14},
  abstract = {In this paper, we discuss the existence and uniqueness of solutions for nonlinear fractional integro-differential equations with the ψ-Caputo fractional derivative under slit-strip integral boundary conditions. Fractional differential equations have been the focus of intense interest, since they can express memory and hereditary properties of various materials and processes in science and engineering. The ψ-Caputo fractional derivative which extends some known fractional operators is a very fruitful instrument for modeling multidimensional dynamical systems and thus applicable to a wide variety of problems. The everything aim of current paper is to get certain sufficient conditions that ensures the multi- solvability as well as uniqueness of the boundary value problem. The study is conducted on the pre-determined space which is a Banach space by using nonlinear functional analysis. In particular, suitable estimates for the nonlinearities involved in the equation are obtained by Hölders inequality and the Mönch fixed-point theorem is the main tool for proving existence of solution. In addition, further conditions are required for ensuring the uniqueness of the obtained solution. The present work contributes to the theory of fractional integro-differential equations with nonlocal boundary conditions and generalizes and improves many results in the literature. The addition of slit-strip integral boundary conditions and the ψ-Caputo fractional derivative results in a more generalized- setting for the study of such types of problems. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the theoretical results and to check the correctness of the theoretical results.},
 year = {2026}
}

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TY  - JOUR
T1  - Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions
AU  - Karthikeyan Panjaiyan
AU  - Manikandan Ambigapathi
Y1  - 2026/10/13
PY  - 2026
N1  - https://doi.org/10.11648/j.iotcc.20261505.14
DO  - 10.11648/j.iotcc.20261505.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 185
EP  - 197
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.iotcc.20261505.14
AB  - In this paper, we discuss the existence and uniqueness of solutions for nonlinear fractional integro-differential equations with the ψ-Caputo fractional derivative under slit-strip integral boundary conditions. Fractional differential equations have been the focus of intense interest, since they can express memory and hereditary properties of various materials and processes in science and engineering. The ψ-Caputo fractional derivative which extends some known fractional operators is a very fruitful instrument for modeling multidimensional dynamical systems and thus applicable to a wide variety of problems. The everything aim of current paper is to get certain sufficient conditions that ensures the multi- solvability as well as uniqueness of the boundary value problem. The study is conducted on the pre-determined space which is a Banach space by using nonlinear functional analysis. In particular, suitable estimates for the nonlinearities involved in the equation are obtained by Hölders inequality and the Mönch fixed-point theorem is the main tool for proving existence of solution. In addition, further conditions are required for ensuring the uniqueness of the obtained solution. The present work contributes to the theory of fractional integro-differential equations with nonlocal boundary conditions and generalizes and improves many results in the literature. The addition of slit-strip integral boundary conditions and the ψ-Caputo fractional derivative results in a more generalized- setting for the study of such types of problems. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the theoretical results and to check the correctness of the theoretical results.
VL  - 15
IS  - 5
ER  -

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Author Information

Karthikeyan Panjaiyan

Department of Mathematics, Sri Vasavi College, Erode, India

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Manikandan Ambigapathi

Department of Mathematics, Sri Vasavi College, Erode, India

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APA Style

Panjaiyan, K., Ambigapathi, M. (2026). Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions. Applied and Computational Mathematics, 15(5), 185-197. https://doi.org/10.11648/j.iotcc.20261505.14

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ACS Style

Panjaiyan, K.; Ambigapathi, M. Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions. Appl. Comput. Math. 2026, 15(5), 185-197. doi: 10.11648/j.iotcc.20261505.14

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AMA Style

Panjaiyan K, Ambigapathi M. Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions. Appl Comput Math. 2026;15(5):185-197. doi: 10.11648/j.iotcc.20261505.14

Copy | Download

@article{10.11648/j.iotcc.20261505.14,
  author = {Karthikeyan Panjaiyan and Manikandan Ambigapathi},
  title = {Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions},
  journal = {Applied and Computational Mathematics},
  volume = {15},
  number = {5},
  pages = {185-197},
  doi = {10.11648/j.iotcc.20261505.14},
  url = {https://doi.org/10.11648/j.iotcc.20261505.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.iotcc.20261505.14},
  abstract = {In this paper, we discuss the existence and uniqueness of solutions for nonlinear fractional integro-differential equations with the ψ-Caputo fractional derivative under slit-strip integral boundary conditions. Fractional differential equations have been the focus of intense interest, since they can express memory and hereditary properties of various materials and processes in science and engineering. The ψ-Caputo fractional derivative which extends some known fractional operators is a very fruitful instrument for modeling multidimensional dynamical systems and thus applicable to a wide variety of problems. The everything aim of current paper is to get certain sufficient conditions that ensures the multi- solvability as well as uniqueness of the boundary value problem. The study is conducted on the pre-determined space which is a Banach space by using nonlinear functional analysis. In particular, suitable estimates for the nonlinearities involved in the equation are obtained by Hölders inequality and the Mönch fixed-point theorem is the main tool for proving existence of solution. In addition, further conditions are required for ensuring the uniqueness of the obtained solution. The present work contributes to the theory of fractional integro-differential equations with nonlocal boundary conditions and generalizes and improves many results in the literature. The addition of slit-strip integral boundary conditions and the ψ-Caputo fractional derivative results in a more generalized- setting for the study of such types of problems. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the theoretical results and to check the correctness of the theoretical results.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Existence Results for ψ-Caputo Fractional Integro-Differential Equations with Strip Boundary Conditions
AU  - Karthikeyan Panjaiyan
AU  - Manikandan Ambigapathi
Y1  - 2026/10/13
PY  - 2026
N1  - https://doi.org/10.11648/j.iotcc.20261505.14
DO  - 10.11648/j.iotcc.20261505.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 185
EP  - 197
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.iotcc.20261505.14
AB  - In this paper, we discuss the existence and uniqueness of solutions for nonlinear fractional integro-differential equations with the ψ-Caputo fractional derivative under slit-strip integral boundary conditions. Fractional differential equations have been the focus of intense interest, since they can express memory and hereditary properties of various materials and processes in science and engineering. The ψ-Caputo fractional derivative which extends some known fractional operators is a very fruitful instrument for modeling multidimensional dynamical systems and thus applicable to a wide variety of problems. The everything aim of current paper is to get certain sufficient conditions that ensures the multi- solvability as well as uniqueness of the boundary value problem. The study is conducted on the pre-determined space which is a Banach space by using nonlinear functional analysis. In particular, suitable estimates for the nonlinearities involved in the equation are obtained by Hölders inequality and the Mönch fixed-point theorem is the main tool for proving existence of solution. In addition, further conditions are required for ensuring the uniqueness of the obtained solution. The present work contributes to the theory of fractional integro-differential equations with nonlocal boundary conditions and generalizes and improves many results in the literature. The addition of slit-strip integral boundary conditions and the ψ-Caputo fractional derivative results in a more generalized- setting for the study of such types of problems. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the theoretical results and to check the correctness of the theoretical results.
VL  - 15
IS  - 5
ER  -

Copy | Download