Effective numerical technique for solving variable order integro-differential equations

A New Numerical Mechanism for Solving Two Models of Variable Order Delay Differential Equations

“…Recently, fractional calculus has received a lot of interest of many researchers; it allows us to analyze integration and differentiation of any order that isn't necessarily an integer. The fractional operator can better describe a variety of real-world phenomena than the integer order calculus [19,1,20]. The most familiar types of the fractional integrals and derivatives are the constant-order (CO) and VO.…”

“… The SFGPs' OM techniques have been proven effectiveness in solving many problems. Ahmed and Melad [8] derived a new SFGOM of differentiation and integration in conjunction with the spectral collocation method to solve VO pantograph-delay differential equations and VO pantograph Volterra delay integrodifferential equations, El-Gindy et al, [19] used different kinds of SFGOMs of the VO differentiation and integration to solve the VO Fredholm-Volterra integro-differential equations, systems of VO-FV-IDEs and VO Volterra partial integro-differential equations, Ahmed and Melad [9] extracted a novel numerical strategy that depends on SFGPs to solve nonlinear singular Emden-Fowler VO-DMs, EL-Kalaawy et al [18] proposed SFGOM of integration to numerically find the solution of fractional variation problems and fractional optimal control problems.…”