2020
DOI: 10.1155/2020/1250970
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Abstract: In this attempt, we introduce a new technique to solve main generalized Abel’s integral equations and generalized weakly singular Volterra integral equations analytically. This technique is based on the Adomian decomposition method, Laplace transform method, and Ψ-Riemann–Liouville fractional integrals. Finally, some examples are proposed and they illustrate the rapidness of our new technical method.

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Cited by 11 publications
(7 citation statements)
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“…This formulation suggests the following iterative scheme for solving the nonlinear Equation (8). Now, for the given initial guess x 0 , the approximate solution is computed by the iterative representation…”
Section: Our Iterative Techniques Proceed With the Following Algorithmsmentioning
confidence: 99%
See 1 more Smart Citation
“…This formulation suggests the following iterative scheme for solving the nonlinear Equation (8). Now, for the given initial guess x 0 , the approximate solution is computed by the iterative representation…”
Section: Our Iterative Techniques Proceed With the Following Algorithmsmentioning
confidence: 99%
“…In most scientific and engineering applications, the problem of finding the solution of nonlinear equations have become an active area of research. Many researchers have explored various order iterative methods to find solutions of the nonlinear equations using various techniques such as homotopy perturbation technique, variational iterative methods and decomposition technique, for details, see [1][2][3][4][5][6][7][8][9][10][11]. Firstly, Traub [12] initiated the study of the iterative methods for the solution of the nonlinear equations and introduced a basic quadratic convergent Newton iterative method for the solution of the nonlinear equations, which have much significance in the literature.…”
Section: Introductionmentioning
confidence: 99%
“…Most of the studies have been devoted to the existence and uniqueness of solutions for fractional differential equations (FDEs); see e.g. [4][5][6][7][8][9]. A fractional differential equation needs a certain inequality to be existent and unique for solution.…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, the subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance due mainly to its demonstrated applications in the mathematical modelling of numerous seemingly diverse and widespread real-life problems in the fields of mathematical, physical, engineering and statistical sciences. Such operators of fractionalorder derivatives as (for example) the Riemann-Liouville fractional derivative and the Liouville-Caputo fractional derivative are found to be potentially useful in the mathematical modelling of many of these problems (see, for example, [1][2][3][4][5][6][7]).…”
Section: Introductionmentioning
confidence: 99%