Fractional Differential and Integral Operators with Respect to a Function

Abdon Atangana is a Professor of applied mathematics at the University of the Free State, Bloemfontein, South Africa.  İlknur Koca is a Professor at Muğla Sıtkı Koçman University, Kötekli/Muğla, Türkiye

• History of differential and integral calculus.-Global derivatives, definitions and properties.- Integral operators, definitions and properties.- Inequalities related to global fractional derivatives.- Inequalities associated to Integrals.- Existence and Uniqueness of IVP with global differentiation on via Picard iteration.- Existence and uniqueness via Carathéodory approach.- Existence and uniqueness analysis of nonlocal global differential equations with expectation approach.- Chaplygin’s method for global differential equations.- Numerical analysis of IVP with classical global derivative.-Numerical analysis of IVP with Riemann-Liouville global derivative.- Numerical analysis of IVP with Caputo-Fabrizio global derivative.- Numerical analysis of IVP with Atangana-Baleanu global derivative.- Examples and applications of global fractional differential equations.