Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions
Restrepo J.E. Ruzhansky M. Suragan D.
15 August 2021Elsevier Inc.
Applied Mathematics and Computation
2021#403
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite series of fractional integro-differential operators, which can be widely and efficiently used for analytic and computational purposes. In the case of constant coefficients, the solution can be expressed in terms of the multivariate Mittag-Leffler functions. In particular, the obtained result extends the Luchko-Gorenflo representation formula [1, Theorem 4.1] to a general class of linear fractional differential equations with variable coefficients, to complex fractional derivatives, and to fractional derivatives with respect to a given function.
Fractional calculus , Fractional differential equations , Fractional integro-differential operators , Mittag-Leffler functions , Variable coefficients
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Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Institute of Mathematics, University of Antioquia, Medellin, Colombia
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, Ghent University, Belgium
School of Mathematical Sciences, Queen Mary University of London, United Kingdom
Department of Mathematics
Institute of Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
School of Mathematical Sciences
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