Numerical approach for solving a class of nonlinear fractional differential equation

It is commonly accepted that fractional differential equations playý ýan important role in the explanation of many physical phenomenaý. ýForý ýthis reason we need a reliable and efficient technique for theý ýsolution of fractional differential equationsý. ýThis paper deals withý ýthe numerical solution of a class of fractional differentialý ýequationý. ýThe fractional derivatives are described based on theý ýCaputo senseý. ýOur main aim is to generalize the Chebyshev cardinalý ýoperational matrix to the fractional calculusý. ýIn this worký, ýtheý ýChebyshev cardinal functions together with the Chebyshev cardinalý ýoperational matrix of fractional derivatives are used for numericalý ýsolution of a class of fractional differential equationsý. ýThe mainý ýadvantage of this approach is that it reduces fractional problems toý ýa system of algebraic equationsý. ýThe method is applied to solveý ýnonlinear fractional differential equationsý. ýIllustrative examplesý ýare included to demonstrate the validity and applicability of theý ýpresented techniqueý.