Common fixed point results via implicit contractions for multi-valued mappings on b-metric like spaces

In this paper, motivated by the recent work [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537] some generalized nonlinear contractive conditions via implicit functions and α-admissible pairs of multi-valued mappings in the setting of b-metric like spaces have been introduced. Some common fixed point results for such mappings in this framework have been provided. Then, some corollaries and consequences for our obtained results are given. Our results are the multi-valued versions of [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537]. An example also is provided to support our obtained results. The presented results generalize and extend some earlier results in the literature

Computational Study of Multiterm Time-Fractional Differential Equation Using Cubic B-Spline Finite Element Method

Due to the symmetry feature in nature, fractional differential equations precisely measure and describe biological and physical processes. Multiterm time-fractional order has been introduced to model complex processes in different physical phenomena. This article presents a numerical method based on the cubic B-spline finite element method for the solution of multiterm time-fractional differential equations. The temporal fractional part is defined in the Caputo sense while the B-spline finite element method is employed for space approximation. In addition, the four-point Gauss−Legendre quadrature is applied to evaluate the source term. The stability of the proposed scheme is discussed by the Von Neumann method, which verifies that the scheme is unconditionally stable. L2 and L∞ norms are used to check the efficiency and accuracy of the proposed scheme. Computed results are compared with the exact and available methods in the literature, which show the betterment of the proposed method

On New Extensions of Darbo's Fixed Point Theorem with Applications

Isik, Huseyin/0000-0001-7558-4088; Parvaneh, Vahid/0000-0002-3820-3351; banaei, shahram/0000-0003-0552-1836; Park, Choonkil/0000-0001-6329-8228WOS:000525824300099In this paper, we extend Darbo's fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results