Browsing by Author "Waqas Ali Faridi"

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    Analysis of non-linear fractional partial differential equations through analytical approach
    (UMT Lahore, 2021) Waqas Ali Faridi
    The main aspire of this desertion is to analyze the partial differential equations with the new extended direct algebraic scheme, and extended (g′/g²)-expansion algorithm in analytical perspective and also mathematical modeling of biological disease in sense of fractional calculus. We analyzed and established novel soliton solutions for different types of partial differential equations in which non-linear directional couplers with the optical meta-materials, the space-time fractional non-linear phi-4 equation, an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics, and the fractional time-space non-linear biological population model. The partial differential equations are reshaped utilizing the different fractional-order derivatives. The soliton solutions of the considered partial differential equations are determined as rapidly convergent sequences with effectively computed by utilizing Mathematica software. The obtained solutions sets are more generalized than the existing solutions as it is transformed into fractional-order derivative because it gives the solutions of problems with heavy tails or infinity fluctuations. Furthermore, the obtained solutions contain almost all types of solitons such as dark, bright, dark-bright, rational, periodic, breather, and singular soliton solutions, etc. The graphical interpretations of obtained solutions are also depicted by allocating the feasible values to unknown constant parameters.