New general single, double and triple conformable integral transforms: Definitions, properties and applications
This study introduces an innovative general adaptive integral transform in single, double and triple types. This article outlines the definitions of these new transformations and establishes their main characteristics in each species. In addition, it examines the connections between newly introduced...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003772 |
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| author | Mohammad Hossein Akrami Abbas Poya Mohammad Ali Zirak |
| author_facet | Mohammad Hossein Akrami Abbas Poya Mohammad Ali Zirak |
| author_sort | Mohammad Hossein Akrami |
| collection | DOAJ |
| description | This study introduces an innovative general adaptive integral transform in single, double and triple types. This article outlines the definitions of these new transformations and establishes their main characteristics in each species. In addition, it examines the connections between newly introduced generic transformations and existing transformations. It is shown that previously developed adaptive transforms, including Laplace, Sumodo, Elzaki, G-transforms, Pourreza, and Aboodh, appear as special cases of this general adaptive transform. Furthermore, the effectiveness of the conformal generalized transform is demonstrated through its application in solving different types of linear and nonlinear fractional differential equations. Such as Black–Scholes and Berger’s equations, to demonstrating its proficiency in this domain. The proposed approach demonstrates versatility by encompassing nearly all conformable integral transforms of orders one, two, and three. As a result, it eliminates the need to derive new formulas for single, double, and triple conformable integral transforms, streamlining the process and enhancing the efficiency of solving related problems. |
| format | Article |
| id | doaj-art-18ab5cde476940e18ebc3e7a134fd223 |
| institution | DOAJ |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-18ab5cde476940e18ebc3e7a134fd2232025-08-20T02:50:09ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210099110.1016/j.padiff.2024.100991New general single, double and triple conformable integral transforms: Definitions, properties and applicationsMohammad Hossein Akrami0Abbas Poya1Mohammad Ali Zirak2Department of Mathematical Science, Yazd University, Yazd, Iran; Corresponding author.Department of Mathematics, Daykondi University, Nili, AfghanistanDepartment of Mathematics, Daykondi University, Nili, AfghanistanThis study introduces an innovative general adaptive integral transform in single, double and triple types. This article outlines the definitions of these new transformations and establishes their main characteristics in each species. In addition, it examines the connections between newly introduced generic transformations and existing transformations. It is shown that previously developed adaptive transforms, including Laplace, Sumodo, Elzaki, G-transforms, Pourreza, and Aboodh, appear as special cases of this general adaptive transform. Furthermore, the effectiveness of the conformal generalized transform is demonstrated through its application in solving different types of linear and nonlinear fractional differential equations. Such as Black–Scholes and Berger’s equations, to demonstrating its proficiency in this domain. The proposed approach demonstrates versatility by encompassing nearly all conformable integral transforms of orders one, two, and three. As a result, it eliminates the need to derive new formulas for single, double, and triple conformable integral transforms, streamlining the process and enhancing the efficiency of solving related problems.http://www.sciencedirect.com/science/article/pii/S2666818124003772Conformable integral transformConformable derivativeIntegral transformsFractional Klein–Gordon equation |
| spellingShingle | Mohammad Hossein Akrami Abbas Poya Mohammad Ali Zirak New general single, double and triple conformable integral transforms: Definitions, properties and applications Partial Differential Equations in Applied Mathematics Conformable integral transform Conformable derivative Integral transforms Fractional Klein–Gordon equation |
| title | New general single, double and triple conformable integral transforms: Definitions, properties and applications |
| title_full | New general single, double and triple conformable integral transforms: Definitions, properties and applications |
| title_fullStr | New general single, double and triple conformable integral transforms: Definitions, properties and applications |
| title_full_unstemmed | New general single, double and triple conformable integral transforms: Definitions, properties and applications |
| title_short | New general single, double and triple conformable integral transforms: Definitions, properties and applications |
| title_sort | new general single double and triple conformable integral transforms definitions properties and applications |
| topic | Conformable integral transform Conformable derivative Integral transforms Fractional Klein–Gordon equation |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003772 |
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