Solution of Time-Variant Fractional Differential Equations With a Generalized Peano–Baker Series

Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives

“…Again, we will refer to the series on the right-hand side of Equation (24) as the generalized Peano-Baker series [14,16]. In view of Lemma 1 and of Equations (9) and (11), the following lemma holds true.…”

“…We will refer to the series on the right-hand side of Equation 14as the generalized Peano-Baker series [14,16]. Assumption 1.…”

“…However, only a few papers are devoted to solutions of the systems of FDEs with variable coefficients and their control. In [14], explicit solutions for the linear systems of initialized [15] FDEs are obtained in terms of generalized Peano-Baker series [16].…”

Solution of Singular Integral Equations via Riemann–Liouville Fractional Integrals

“…Fractional dynamic varying systems with singular kernels either in the Riemann-Liouville sense or in the Caputo sense have been investigated in the literature [1][2][3]. To solve a fractional dynamic equation, we always apply a corresponding fractional integral operator.…”

“…Recently, Wazwaz [4,5] solved integral equations ( 1) and (2). Unlike [4,5], in the present paper, we are going to introduce a new technique, which is based on the Adomian decomposition method, Laplace transform method, and Ψ-Riemann-Liouville fractional integrals, for solving main generalized Abel's integral equations and generalized weakly singular Volterra integral equations.…”