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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Main Author: McSylvester Ejighikeme Omaba
Format: Article
Language:English
Published: Elsevier 2025-03-01
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.
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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