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Abstract Recent research by physicists and mathematicians has revealed that many fundamental dynamical processes exhibit behaviour of fractional order that can depend on space and/or time. This shows that variable order calculus provides a valuable mathematical framework for describing intricate dynamical problems. It is new topic at mathematical world we dealt with a study it during this thesis. This thesis developed the SCM with several types of OMs of the VO fractional derivatives and integrals of SFGPs for solving different VOFuDEs based on the SFGPs. The suggested VOFuDEs exemplify a number of equations with significant applications, including VO-DDEs with ICs or IFC, VO-NFuDEs, VO-P-DDEs, VO-PV-DIDEs, VO-EFDDEs, VO-PDDEs with ICs and BCs, VO-PDDEs with IFC and BCs finally VO-FV-IDEs. |