THE FUZZY LAPLACE TRANSFORM METHOD FOR SOLVING FUZZY DYNAMIC EQUATIONS ON TIME SCALES

Published 31 July 2021 •  vol 14  •  no 2  • 


Authors:

 

Vasavi Ch, Department of Mathematics Koneru Lakshmaiah Education Foundation, Vaddeswaram, A.P., India
Srinivasa Rao T, Department of Mathematics Koneru Lakshmaiah Education Foundation, Vaddeswaram, A.P., India
Suresh Kumar G, Department of Mathematics Koneru Lakshmaiah Education Foundation, Vaddeswaram, A.P., India
Venkata Naresh Mandhala, Department of Computer Science and Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, A.P., India

Abstract:

 

In this paper, we develop the calculus of fuzzy Laplace transforms on time scales T under generalized Hukuhara delta derivative for the fuzzy valued functions of real variables on time scales whose values are convex, upper semi-continuous, normal, and compactly supported fuzzy sets in R. By incorporating the calculus of Fuzzy Laplace transforms on dynamic equations on time scales under generalized Hukuhara delta derivative leading to Fuzzy Laplace transforms on time scales. We studied the fundamental properties and related theorems which help to establish the relation between the fuzzy Laplace transforms of a fuzzy valued function on time scales and generalized Hukuhara delta derivative. By using these results, we can provide solutions to FDEs which reduces the problem of solving an FDE to an algebraic problem. These results also have the advantage that it solves problems directly, without first determining a general solution. On the other hand, the concept of dynamic equations on time scales unifies the calculus of both differential and difference equations and hence these results generalize the results of fuzzy Laplace transforms on fuzzy differential and difference calculus. There are many other time scales than set of reals and integers, hence one can get much more general result. All the results are illustrated with suitable examples.

Keywords:

 

Fuzzy Laplace Transforms; Time Scale; Fuzzy Dynamic Equation; Generalized Hukuhara Delta Derivative

References:

 

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Citations:

 

APA:
Vasavi, C., Srinivasa, R. T., Suresh, K. G., & Mandhala, V. N. (2021). The Fuzzy Laplace Transform Method for Solving Fuzzy Dynamic Equations on Time Scales. International Journal of Grid and Distributed Computing (IJGDC), ISSN: 2005-4262 (Print); 2207-6379 (Online), NADIA, 14(2), 1-14. doi: 10.33832/ijgdc.2021.14.2.01.

MLA:
Vasavi, Ch, et al. “The Fuzzy Laplace Transform Method for Solving Fuzzy Dynamic Equations on Time Scales.” International Journal of Grid and Distributed Computing (IJGDC), ISSN: 2005-4262 (Print); 2207-6379 (Online), NADIA, vol. 14, no. 2, 2021, pp. 1-14. IJGDC, http://article.nadiapub.com/IJGDC/vol14_no2/1.html.

IEEE:
[1] C. Vasavi, R. T. Srinivasa, S. Kumar G, and Mandhala, V. N., "The Fuzzy Laplace Transform Method for Solving Fuzzy Dynamic Equations on Time Scales.." International Journal of Grid and Distributed Computing (IJGDC), ISSN: 2005-4262 (Print); 2207-6379 (Online), NADIA, vol. 14, no. 2, pp. 1-14, July 2021.