In this paper, we introduce a class of generalized quasivariational inclusions and show its equivalence with a class of fixed point problems by making use of the properties of proximal maps. Using this equivalence, we develop the Mann and Ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions. Further, using fixed point techniques, we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms. Our algorithms and results improve and generalize many known corresponding algorithms and results.ᮊ 1997 Academic Press
In the present work, an efficient numerical technique, called q-homotopy analysis transform method (briefly, q-HATM), is applied to nonlinear Fisher's equation of fractional order. The homotopy polynomials are employed, in order to handle the nonlinear terms. Numerical examples are illustrated to examine the efficiency of the proposed technique. The suggested algorithm provides the auxiliary parameters ℏ and n , which help us to control and adjust the convergence region of the series solution. The outcomes of the study reveal that the q-HATM is computationally very effective and accurate to analyse nonlinear fractional differential equations.
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