Aboodh transform iterative method Adomian decomposition method Atangana–Baleanu fractional derivative Babenko’s approach Banach fixed point theorem Bessel polynomials Caputo derivative Caputo fractional derivative Caputo q-derivative Caputo–Fabrizio and Atangana-Baleanu operators Euler–Lagrange equation Fredholm–Volterra integral Equations Gelfand problem Green’s function HHF type inequality MHD equations Mathematics & science Mittag–Leffler function Research & information: general Riemann–Liouville derivative Riemann–Liouville fractional difference operator Riemann–Liouville q-integral Shehu decomposition method Shehu transform Sonine kernel Ulam stability anisotropic Lorentz space approximate endpoint criterion approximate solutions bilateral tempered fractional derivative