Fractional Calculus and Special Functions with Applications

• Other Authors: Özarslan, Mehmet Ali (Editor), Fernandez, Arran (Editor), Area, Ivan (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: Research & information: general; Mathematics & science; Caputo-Hadamard fractional derivative; coupled system; Hadamard fractional integral; boundary conditions; existence; fixed point theorem; fractional Langevin equations; existence and uniqueness solution; fractional derivatives and integrals; stochastic processes; calculus of variations; Mittag-Leffler functions; Prabhakar fractional calculus; Atangana-Baleanu fractional calculus; complex integrals; analytic continuation; k-gamma function; k-beta function; Pochhammer symbol; hypergeometric function; Appell functions; integral representation; reduction and transformation formula; fractional derivative; generating function; physical problems; fractional derivatives; fractional modeling; real-world problems; electrical circuits; fractional differential equations; fixed point theory; Atangana-Baleanu derivative; mobile phone worms; fractional integrals; Abel equations; Laplace transforms; mixed partial derivatives; second Chebyshev wavelet; system of Volterra-Fredholm integro-differential equations; fractional-order Caputo derivative operator; fractional-order Riemann-Liouville integral operator; error bound; n/a
• Online Access: DOAB: download the publication; DOAB: description of the publication

The study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications because of their properties of interpolation between integer-order operators. This field includes classical fractional operators such as Riemann-Liouville, Weyl, Caputo, and Gr...