On linear fractional differential equations with variable coefficients

Fernandez A. Restrepo J.E. Suragan D.
1 November 2022 Elsevier Inc.

Applied Mathematics and Computation
2022 #432

We study and solve linear ordinary differential equations, with fractional order derivatives of either Riemann–Liouville or Caputo types, and with variable coefficients which are either integrable or continuous functions. In each case, the solution is given explicitly by a convergent infinite series involving compositions of fractional integrals, and its uniqueness is proved in suitable function spaces using the Banach fixed point theorem. As a special case, we consider the case of constant coefficients, whose solutions can be expressed by using the multivariate Mittag–Leffler function. Some illustrative examples with potential applications are provided.

Caputo fractional derivative , Fixed point theory , Fractional differential equations , Mittag–Leffler functions , Riemann–Liouville fractional calculus , Series solutions

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Department of Mathematics, Eastern Mediterranean University, via Mersin-10, Northern Cyprus, Turkey
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium

Department of Mathematics
Department of Mathematics
Department of Mathematics: Analysis

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