To investigate a class of multi-singular pointwise defined fractional $ q $–integro-differential equation with applications

Mohammad Esmael Samei; Lotfollah Karimi; Mohammed K. A. Kaabar; Mohammad Esmael Samei; Lotfollah Karimi; Mohammed K. A. Kaabar

doi:10.3934/math.2022437

AIMS Mathematics

2022, Volume 7, Issue 5: 7781-7816. doi: 10.3934/math.2022437

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To investigate a class of multi-singular pointwise defined fractional $ q $–integro-differential equation with applications

1.
Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran
2.
Department of Mathematics, Hamedan University of Technology, Hamedan, Iran
3.
Jabalia Camp, United Nations Relief and Works Agency (UNRWA), Palestinian Refugee Camp, Gaza Strip Jabalya, Palestine
4.
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia

Received: 06 November 2021 Revised: 03 February 2022 Accepted: 14 February 2022 Published: 17 February 2022
MSC : 34A08, 34B16, 39A13

In the research work, we discuss a multi-singular pointwise defined fractional $ q $–integro-differential equation under some boundary conditions via the Riemann-Liouville $ q $–integral and Caputo fractional $ q $–derivatives. New existence results rely on the $ \alpha $-admissible map and fixed point theorem for $ \alpha $-$ \mathtt{ψ} $-contraction map. At the end, we present an example with application and some algorithms to illustrate the primary effects.
- singularity,
- pointwise defined equations,
- integral boundary conditions,
- Caputo $ q $–derivation
Citation: Mohammad Esmael Samei, Lotfollah Karimi, Mohammed K. A. Kaabar. To investigate a class of multi-singular pointwise defined fractional $ q $–integro-differential equation with applications[J]. AIMS Mathematics, 2022, 7(5): 7781-7816. doi: 10.3934/math.2022437

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Abstract

In the research work, we discuss a multi-singular pointwise defined fractional $ q $–integro-differential equation under some boundary conditions via the Riemann-Liouville $ q $–integral and Caputo fractional $ q $–derivatives. New existence results rely on the $ \alpha $-admissible map and fixed point theorem for $ \alpha $-$ \mathtt{ψ} $-contraction map. At the end, we present an example with application and some algorithms to illustrate the primary effects.

References

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