Solution of fuzzy singular integral equation with Abel’s type kernel using a novel hybrid method

Abstract

In this paper, we are applying a novel analytical hybrid method to find the solution of a fuzzy Volterra Abel's integral equation of the second kind. The fuzzy number is used in its parametric form under which the fuzzy Volterra Abel's integral equation will be converted into a system of integral equations as in a crisp case. Moreover, to solve the general fuzzy Volterra integral equation with Abel's type kernel, and to show that the proposed method is efficient, a few accurate and simple examples are given for the demonstration of our results. MSC: Primary 45Exx; 45E10; secondary 47B35

Applications of Double Fuzzy Sumudu Adomain Decompositon Method for Two-dimensional Volterra Fuzzy Integral Equations

“…Some properties of Sumudu transform and double Sumudu transform in [9,10,22]. The convolution theorem is provided below.…”

“…Bushnaq at al. [9] find solution a fuzzy Volterra Abel's integral equation of the second kind with Laplace -ADM. Georgieva [4,5,14], gave solution two dimensional fuzzy Volterra-Fredholm with Adomain and use double fuzzy Sumudu Transform to solve partial Volterra Fuzzy Integro-Differential Equations and fuzzy Sawi decompositon for nonlinear differential equations. L. Al-Taee at al.…”

Novel Numerical Investigations of Fuzzy Cauchy Reaction–Diffusion Models via Generalized Fuzzy Fractional Derivative Operators

“…They demonstrated two novel existence theorems for fuzzy fractional differential equations using Riemann-Liouville generalized H-differentiability as well as fuzzy Nagumo and Krasnoselskii-Krein criteria [31]. Bushneq et al [32] explored the findings of a fuzzy singular integral equation with an Abel type kernel using a novel hybrid method. In [33], Zia et al adopted a semi-analytical technique for finding the solutions to fuzzy nonlinear integral equations.…”

“…Bushneq et al [32] explored the findings of a fuzzy singular integral equation with an Abel type kernel using a novel hybrid method. In [33], Zia et al adopted a semi-analytical technique for finding the solutions to fuzzy nonlinear integral equations. Salahshour et al [34] expounded the H-differentiability with Laplace transform to solve the FDEs.…”

On solution of fuzzy Volterra integro-differential equations

“…Many scholars have contributed, to investigate and studying solutions of FIDEs and FIEs utilizing different numerical and analytical techniques. These techniques include the iterative approximation technique (Abigail, 2019), He's homotopy perturbation method (Sekar & Thirumurugan, 2019), Laplace Adomian Decomposition method (Bushnaq, Ullah, Ullah, & Shah, 2020;Ullah, Ullah, Abdeljawad, Hammouch, & Shah, 2021;Ullah, Ullah, Shah, & Baleanu, 2020), Sumudu decomposition method (Kang, Iqbal, Habib, & Nazeer, 2019), fuzzy differential transform method (Biswas & Roy, 2018), and Kernel Hilbert space method (Gumah, Naser, Al-Smadi, & Al-Omari, 2018), and others (Hooshangian, 2019). The scholars also investigated the existence and the uniqueness of the solution for FIDEs and FIEs (Ali, 2018;Georgieva, 2020;Sindu Devi & Ganesan, 2018;Tunc¸& Tunc¸, 2018).…”