Browsing by Author "Shah, K."

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Citation Count: Ullah, Z...et al. (2020). "Computation of semi-analytical solutions of fuzzy nonlinear integral equations", Advances in Difference Equations, Vol. 2020, No. 1.
Computation of semi-analytical solutions of fuzzy nonlinear integral equations
(2020) Ullah, Z.; Ullah, A.; Shah, K.; Baleanu, Dumitru; 56389
In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A hybrid method of Laplace transform coupled with Adomian decomposition method is used to find the solution of the fuzzy nonlinear integral equations including fuzzy nonlinear Fredholm integral equation, fuzzy nonlinear Volterra integral equation, and fuzzy nonlinear singular integral equation of Abel type kernel. We also provide some suitable examples to better understand the proposed method. © 2020, The Author(s).
Citation Count: Jarad, Fahd; Abdeljawad, Thabet; Shah, K. (2020). "On the weighted fractional operators of a function with respect to another function", Fractals, Vol. 28, No. 8.
On the weighted fractional operators of a function with respect to another function
(2020) Jarad, Fahd; Abdeljawad, Thabet; Shah, K.; 234808
The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators. © The Author(s)
Citation Count: Eiman...at all (2020). "Study on Krasnoselskii's fixed point theorem for Caputo-Fabrizio fractional differential equations", Advances in Difference Equations, Vol. 2020, No. 1.
Study on Krasnoselskii's fixed point theorem for Caputo-Fabrizio fractional differential equations
(2020) Eiman; Shah, K.; Sarwar, M.; Baleanu, Dumitru; 56389
This note is concerned with establishing existence theory of solutions to a class of implicit fractional differential equations (FODEs) involving nonsingular derivative. By using usual classical fixed point theorems of Banach and Krasnoselskii, we develop sufficient conditions for the existence of at least one solution and its uniqueness. Further, some results about Ulam-Hyers stability and its generalization are also discussed. Two suitable examples are given to demonstrate the results.
Citation Count: Ali, A.; Shah, K.; Baleanu, D., "Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations",Advances in Difference Equations, (January 2019).
Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations
(Pushpa Publishing House, 2019) Ali, Arshad; Shah, K.; Baleanu, Dumitru; 56389
In this paper, we derive some sufficient conditions which ensure the existence and uniqueness of a solution for a class of nonlinear three point boundary value problems of fractional order implicit differential equations (FOIDEs) with some boundary and impulsive conditions. Also we investigate various types of Hyers-Ulam stability (HUS) for our concerned problem. Using classical fixed point theory and nonlinear functional analysis, we obtain the required conditions. In the last section we give an example to show the applicability of our obtained results.