APPLICATION OF FIXED POINT THEOREM IN THE SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS: A COMPLEX VALUED APPROACH*
By
Sopan Raosaheb Shinde and Renu Praveen Pathak
Department of Mathematics, Sandip University, Nashik, Maharashtra, India-422213
Email: scholarswapnil@gmail.com, renupathak380@gmail.com
(Received: February 23, 2023; In format: February 26, 2023; Revised : December 04, 2023; Accepted : December 06, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53235
Abstract
It's remarkable to note that Complex valued Integro-differential and integral type equations are currently intensifying the attention of appreciable researchers due to their comprehensive applications. Thus, this study is fully devoted to the application part of the complex valued controlled, double controlled metric ∂c. We introduce an extended version of the Fisher and Banach type contraction theorem and present some examples to sustain our results. As part of the main theorem's application, we address a common solution with uncertainty in two different folds as follows: [I] Applying the fractional Adams-Bashforth method to the (1.1) FVIdE. [II] Applying it to the integral type equation (1.2) in the setting of the Extended complex valued metric space.
2020 Mathematical Science Classification: 47H09,24H25,34A08,47H10.
Keywords and Phrases: Atangana Baleanu Fractional integral operator, fredholm Volterra integro-differential equation(FVIdE), Complex valued metric space(CVMS), Common fixed point, Cauchy sequence, Contractive condition and completeness.