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This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention.

bessel function --- harmonically convex function --- non-singular function involving kernel fractional operator --- Hadamard inequality --- Fejér–Hadamard inequality --- Elzaki transform --- Caputo fractional derivative --- AB-fractional operator --- new iterative transform method --- Fisher’s equation --- Hukuhara difference --- Atangana–Baleanu fractional derivative operator --- Mittag–Leffler kernel --- Fornberg–Whitham equation --- fractional div-curl systems --- Helmholtz decomposition theorem --- Riemann–Liouville derivative --- Caputo derivative --- fractional vector operators --- weighted (k,s) fractional integral operator --- weighted (k,s) fractional derivative --- weighted generalized Laplace transform --- fractional kinetic equation --- typhoid fever disease --- vaccination --- model calibration --- asymptotic stability --- fixed point theory --- nonlinear models --- efficiency index --- computational cost --- Halley’s method --- basin of attraction --- computational order of convergence --- Caputo–Hadamard fractional derivative --- thermostat modeling --- Caputo–Hadamard fractional integral --- hybrid Caputo–Hadamard fractional differential equation and inclusion --- prey-predator model --- boundedness --- period-doubling bifurcation --- Neimark-Sacker bifurcation --- hybrid control --- fractal dimensions --- cubic B-splines --- trigonometric cubic B-splines --- extended cubic B-splines --- Caputo–Fabrizio derivative --- Cattaneo equation --- Hermite-Hadamard-type inequalities --- Hilfer fractional derivative --- Hölder’s inequality --- fractional-order differential equations --- operational matrices --- shifted Vieta–Lucas polynomials --- Adomian decomposition method --- system of Whitham-Broer-Kaup equations --- Caputo-Fabrizio derivative --- Yang transform --- ϑ-Caputo derivative --- extremal solutions --- monotone iterative method --- sequences --- convex --- exponential convex --- fractional --- quantum --- inequalities --- Gould-Hopper-Laguerre-Sheffer matrix polynomials --- quasi-monomiality --- umbral calculus --- fractional calculus --- Euler’s integral of gamma functions --- beta function --- generalized hypergeometric series --- operational methods --- delta function --- Riemann zeta-function --- fractional transforms --- Fox–Wright-function --- generalized fractional kinetic equation --- n/a --- Fejér-Hadamard inequality --- Fisher's equation --- Atangana-Baleanu fractional derivative operator --- Mittag-Leffler kernel --- Fornberg-Whitham equation --- Riemann-Liouville derivative --- Halley's method --- Caputo-Hadamard fractional derivative --- Caputo-Hadamard fractional integral --- hybrid Caputo-Hadamard fractional differential equation and inclusion --- Hölder's inequality --- shifted Vieta-Lucas polynomials --- Euler's integral of gamma functions --- Fox-Wright-function