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fractional derivative; generalized Mittag-Leffler kernel (GMLK); Legendre polynomials; Legendre spectral collocation method; dynamical systems; random time change; inverse subordinator; asymptotic behavior; Mittag–Leffler function; data fitting; magnetization; magnetic fluids; Gamma function; Psi function; Pochhammer symbol; hypergeometric function 2F1; generalized hypergeometric functions tFu; Gauss’s summation theorem for 2F1(1); Kummer’s summation theorem for 2F1(−1); generalized Kummer’s summation theorem for 2F1(−1); Stirling numbers of the first kind; Hilfer–Hadamard fractional derivative; Riemann–Liouville fractional derivative; Caputo fractional derivative; fractional differential equations; inclusions; nonlocal boundary conditions; existence and uniqueness; fixed point; gamma function; Beta function; Mittag-Leffler function; Generalized Mittag-Leffler functions; generalized hypergeometric function; Fox–Wright function; recurrence relations; Riemann–Liouville fractional calculus operators; (α, h-m)-p-convex function; Fejér–Hadamard inequality; extended generalized fractional integrals; Mittag–Leffler functions; initial value problems; Laplace transform; exact solution; Chebyshev inequality; Pólya-Szegö inequality; fractional integral operators; Wright function; Srivastava’s polynomials; fractional calculus operators; Lavoie–Trottier integral formula; Oberhettinger integral formula; fractional partial differential equation; boundary value problem; separation of variables; Mittag-Leffler; Abel-Gontscharoff Green’s function; Hermite-Hadamard inequalities; convex function; κ-Riemann-Liouville fractional integral; Dirichlet averages; B-splines; dirichlet splines; Riemann–Liouville fractional integrals; hypergeometric functions of one and several variables; generalized Mittag-Leffler type function; Srivastava–Daoust generalized Lauricella hypergeometric function; fractional calculus; Hermite–Hadamard inequality; Fox H function; subordinator and inverse stable subordinator; Lamperti law; order statistic; n/a