On the solutions of nonlinear Caputo–Fabrizio fractional partial differential equations arising in applied mathematics

JPRM-Vol. 18 (2022), Issue 2, pp. 42 – 54 Open Access Full-Text PDF
Ali Khalouta
Abstract: This paper proposes a new semi-analytical method known as the variational iteration transform method (VITM) to obtain the solutions of the nonlinear Caputo–Fabrizio fractional partial differential equations arising in applied mathematics. For nonlinear equations in general, there is no method that gives an exact solution and, therefore, only approximate analytical solutions can be derived by using procedures such as linearization or perturbation. This method is combined form of the Aboodh transform and the variational iteration method. The advantage of VITM is the simplicity of the computations and the non-requirement of linearization or smallness assumptions. Moreover, this method enables us to overcome the difficulties arising in identifying the general Lagrange multiplier. For further illustrations of the efficiency and reliability of VITM, some numerical applications are pesented. The numerical results showed that the proposed method is efficient and precise to obtain the solutions of nonlinear fractional partial differential equations.
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On Split Equilibrium and Fixed Point Problems for Finite Family of Bregman Quasi-Nonexpansive Mappings in Banach spaces

JPRM-Vol. 18 (2022), Issue 2, pp. 23 – 41 Open Access Full-Text PDF
H. A. Abass, O. K. Narain, K. O. Oyewole, U. O. Adiele
Abstract: In this paper, we introduce a trifunction split equilibrium problem using a generalized relaxed α-monotonicity in the framework of p-uniformly convex and uniformly smooth Banach spaces. We develop an iterative algorithm for approximating a common solution of split equilibrium problem and fixed point problem for finite family of Bregman quasi-nonexpansive mappings. Using our iterative algorithm, we state and prove a strong convergence theorem for approximating a common solution of the aforementioned problems. Our iterative scheme is design in such a way that it does not require any knowledge of the operator norm. We display a numerical example to show the applicability of our result. Our result extends and complements some related results in literature.
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Generalized Identities and Inequalities of Čebyšev and Ky Fan Type for ∇−convex function

JPRM-Vol. 18 (2022), Issue 2, pp. 1 – 22 Open Access Full-Text PDF
Faraz Mehmood , Asif R. Khan
Abstract: In the present article we establish three generalizations, first generalization is related to discrete Čebyšev identity for function of higher order ∇ divided difference with two independent variables and give its special case as a sequence of higher order ∇ divided difference. Moreover, we deduce results of discrete inequality of Čebyšev involving higher order ∇−convex function. The second and third generalizations are for integral Čebyšev and integral Ky Fan identities for function of higher order derivatives with two independent variables and discuss its inequalities using ∇−convex function. Generalized results give similar results of Pěcari´c’s article [23] and recapture some established results.
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