Duality of Shehu transform with other well known transforms and application to fractional order differential equations
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Summary
This summary is machine-generated.Researchers explore duality relations between the Shehu transform and other integral transforms like Laplace and Fourier. These connections simplify solving complex differential and fractional equations, saving valuable research time.
Area Of Science
- Mathematics
- Applied Science
- Engineering
Background
- Integral transforms are crucial tools in applied science and engineering.
- Researchers often face challenges applying specific transforms to differential and integral equations.
- The Shehu transform exhibits convergence properties to other known integral transforms by adjusting parameters.
Purpose Of The Study
- To derive inter-conversion (duality) relations between the Shehu transform and several other integral transforms.
- To establish a framework for simplifying the application of integral transforms in problem-solving.
- To highlight the utility of these duality relations in addressing complex mathematical challenges.
Main Methods
- Derivation of duality relations between the Shehu transform and Natural, Sumudu, Laplace, Laplace-Carson, Fourier, Aboodh, Elzaki, Kamal, and Mellin transforms.
- Analysis of the properties and implications of these newly derived relations.
- Demonstration of the ease of solving differential equations using these inter-conversion properties.
Main Results
- Established comprehensive duality relations connecting the Shehu transform with multiple other integral transforms.
- Demonstrated that these relations simplify the process of solving differential and integral equations, especially when direct application of a transform is complex.
- Showcased the potential for easier visualization and application in solving fractional order differential equations.
Conclusions
- The derived duality relations offer a significant advantage for researchers by simplifying complex mathematical problems.
- These relations enhance the applicability and ease of use of various integral transforms, including the Shehu transform.
- The findings contribute to more efficient problem-solving in applied mathematics, science, and engineering, particularly for fractional calculus.
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