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|Title:||Efficacious Algorithms for the Solutions of Fractional Differential Equations|
|Publisher:||University of the Punjab , Lahore|
|Abstract:||Fractional calculus is the generalization of integer-order calculus to non-integer order. In recent decades, fractional calculus has re-attracted the attention of scientists and engineers. Due to the nonlocal property, fractional operators give a perfect aid to characterize the memory and hereditary properties of various processes and materials. As a result, and motivated by the increasingly important role played by fractional calculus, mathematicians are constantly developing algorithms for solving fractional diﬀerential equations. The objective of this work is to develop the eﬃcacious algorithms for the solutions of both ordinary and partial fractional diﬀerential equations. For solving both linear and non-linear fractional diﬀerential equations, spline method and residual power series method are used. Matlab, Maple and Mathematica programmes are developed to compute the numerical solutions. The simplicity, eﬃciency and accuracy of the presented methods are demonstrated by aid of several examples and comparisons are made between exact and numerical solutions.|
|Gov't Doc #:||15188|
|Appears in Collections:||PhD Thesis of All Public / Private Sector Universities / DAIs.|
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