Non Probabilistic Solution of Fuzzy Fractional Fornberg-Whitham Equation

Fractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain fractional Fornberg-Whitham equation. Using the single parametric form of fuzzy numbers, original fuzzy fractional Fornberg-Whitham equation is converted first to an interval based fuzzy differential equation. Next this equation is transformed to crisp form by applying the proposed double parametric form of fuzzy numbers. Finally it has been solved using homotopy perturbation method (HPM). Present method performs very well in terms of computational efficiency. The reliability of the method is shown by obtaining an approximate numerical solution for different cases. Results are given in term of plots and are also compared in special cases.