Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives

By Myong-Ha Kim, Guk-Chol Ri, H. O. Fractional Calculus and Applied Analysis, 2013

48 citations recorded by the source corpus.

This paper provides results on the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski’s type. We prove that the initial value problem has the solution if and only if some initial values are zero.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/643e7e5275bf06dfb42cad10a17abf458623b029

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

NONLOCAL PROBLEM FOR A MIXED TYPE FOURTH-ORDER DIFFERENTIAL EQUATION WITH HILFER FRACTIONAL OPERATOR (2020, methodology): “In [15], a solution was found by the operational calculus for a problem more general than (2.”
Modified Galerkin algorithm for solving multitype fractional differential equations (2019, background): “k=0 (−1)i+j−k(k + n)!Γ(γ + j + 1)Γ(δ + i + 1)Γ(k + γ + δ + i + 1)Γ(k + n + δ + 1 − νn)(νn − k − n)j k!j!(i − k)!Γ(k + δ + 1)Γ(γ + δ + i + 1)Γ(k + n + 1 − νn)Γ(k + n + γ + δ + j + 2 − νn) , (18)”