Growth estimates of solutions to fractional hybrid partial differential equations
We investigate a class of fractional hybrid partial differential equations subject to both linear and quadratic perturbations. By imposing a Lipschitz continuity condition on the third variable of the non-linear functions, we establish the well–posedness of the equations’ solutions by applying the B...
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000683 |
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| author | McSylvester Ejighikeme Omaba |
| author_facet | McSylvester Ejighikeme Omaba |
| author_sort | McSylvester Ejighikeme Omaba |
| collection | DOAJ |
| description | We investigate a class of fractional hybrid partial differential equations subject to both linear and quadratic perturbations. By imposing a Lipschitz continuity condition on the third variable of the non-linear functions, we establish the well–posedness of the equations’ solutions by applying the Banach fixed–point theorem. The growth estimates of solutions to these perturbation equations are derived using the non-linear weakly singular fractional integral inequality of the Wendroff type. Additionally, the growth behaviors for both types of equations are analyzed, and the result shows that they exhibit some exponential growth rates. It is further noted that the proofs of the equations’ properties entail varying degrees of difficulty and requiring additional conditions. Several numerical examples are presented to provide insights and highlight the significance of our results. |
| format | Article |
| id | doaj-art-5ef9a73052cf44319f742ca856e72f53 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-5ef9a73052cf44319f742ca856e72f532025-08-20T01:57:51ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-011310114110.1016/j.padiff.2025.101141Growth estimates of solutions to fractional hybrid partial differential equationsMcSylvester Ejighikeme Omaba0Department of Mathematics, College of Science, University of Hafr Al Batin, Hafr Al Batin, P.O. Box 1803, Hafr Al Batin 31991, Eastern Region, Saudi ArabiaWe investigate a class of fractional hybrid partial differential equations subject to both linear and quadratic perturbations. By imposing a Lipschitz continuity condition on the third variable of the non-linear functions, we establish the well–posedness of the equations’ solutions by applying the Banach fixed–point theorem. The growth estimates of solutions to these perturbation equations are derived using the non-linear weakly singular fractional integral inequality of the Wendroff type. Additionally, the growth behaviors for both types of equations are analyzed, and the result shows that they exhibit some exponential growth rates. It is further noted that the proofs of the equations’ properties entail varying degrees of difficulty and requiring additional conditions. Several numerical examples are presented to provide insights and highlight the significance of our results.http://www.sciencedirect.com/science/article/pii/S2666818125000683Fractional hybrid PDEWell–posednessGrowth estimatesWendroff–type inequalityQuadratic perturbationQuadratic integral |
| spellingShingle | McSylvester Ejighikeme Omaba Growth estimates of solutions to fractional hybrid partial differential equations Partial Differential Equations in Applied Mathematics Fractional hybrid PDE Well–posedness Growth estimates Wendroff–type inequality Quadratic perturbation Quadratic integral |
| title | Growth estimates of solutions to fractional hybrid partial differential equations |
| title_full | Growth estimates of solutions to fractional hybrid partial differential equations |
| title_fullStr | Growth estimates of solutions to fractional hybrid partial differential equations |
| title_full_unstemmed | Growth estimates of solutions to fractional hybrid partial differential equations |
| title_short | Growth estimates of solutions to fractional hybrid partial differential equations |
| title_sort | growth estimates of solutions to fractional hybrid partial differential equations |
| topic | Fractional hybrid PDE Well–posedness Growth estimates Wendroff–type inequality Quadratic perturbation Quadratic integral |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000683 |
| work_keys_str_mv | AT mcsylvesterejighikemeomaba growthestimatesofsolutionstofractionalhybridpartialdifferentialequations |