A study on the existence of numerical and analytical solutions for fractional integrodifferential equations in Hilfer type with simulation

Reny George; Seher Melike Aydogan; Fethiye Muge Sakar; Mehran Ghaderi; Shahram Rezapour; Reny George; Seher Melike Aydogan; Fethiye Muge Sakar; Mehran Ghaderi; Shahram Rezapour

doi:10.3934/math.2023541

AIMS Mathematics

2023, Volume 8, Issue 5: 10665-10684. doi: 10.3934/math.2023541

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A study on the existence of numerical and analytical solutions for fractional integrodifferential equations in Hilfer type with simulation

1.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2.
Department of Mathematics and Computer Science, St. Thomas College, Bhilai, Chhattisgarth 49006, India
3.
Department of Mathematics, Istanbul Technical University, Istanbul, Turkey
4.
Department of Management, Dicle University, Diyarbakir, Turkey
5.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
6.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
7.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 06 January 2023 Revised: 14 February 2023 Accepted: 19 February 2023 Published: 03 March 2023
MSC : 34A08, 34A12

Previous studies have shown that fractional derivative operators have become an integral part of modeling natural and physical phenomena. During the progress and evolution of these operators, it has become clear to researchers that each of these operators has special capacities for investigating phenomena in engineering sciences, physics, biological mathematics, etc. Fixed point theory and its famous contractions have always served as useful tools in these studies. In this regard, in this work, we considered the Hilfer-type fractional operator to study the proposed integrodifferential equation. We have used the capabilities of measure theory and fixed point techniques to provide the required space to guarantee the existence of the solution. The Schauder and Arzela-Ascoli theorems play a fundamental role in the existence of solutions. Finally, we provided two examples with some graphical and numerical simulation to make our results more objective.
- fractional integrodifferential equation,
- Hilfer derivative,
- fixed point,
- generalized Riemann-Liouville fractional derivative
Citation: Reny George, Seher Melike Aydogan, Fethiye Muge Sakar, Mehran Ghaderi, Shahram Rezapour. A study on the existence of numerical and analytical solutions for fractional integrodifferential equations in Hilfer type with simulation[J]. AIMS Mathematics, 2023, 8(5): 10665-10684. doi: 10.3934/math.2023541

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Abstract

Previous studies have shown that fractional derivative operators have become an integral part of modeling natural and physical phenomena. During the progress and evolution of these operators, it has become clear to researchers that each of these operators has special capacities for investigating phenomena in engineering sciences, physics, biological mathematics, etc. Fixed point theory and its famous contractions have always served as useful tools in these studies. In this regard, in this work, we considered the Hilfer-type fractional operator to study the proposed integrodifferential equation. We have used the capabilities of measure theory and fixed point techniques to provide the required space to guarantee the existence of the solution. The Schauder and Arzela-Ascoli theorems play a fundamental role in the existence of solutions. Finally, we provided two examples with some graphical and numerical simulation to make our results more objective.

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