Existence of solutions for a coupled system of three-point fractional order boundary value problems

Abstract

In this paper, we establish the existence of a solution for a coupled system of threepoint fractional order boundary value problems by applying the Schauder fixed point theorem in a Banach space under suitable conditions.Mathematics subject classification (2010): 34A34, 34B15.

The effect of fractional calculus on the formation of quantum‐mechanical operators

“…Namely, for a function , the (conformable) fractional derivative of order 0< α ≤ 1 of f at t >0 was defined by and the fractional derivative at 0 is introduced as . Some application of this type of fractional derivative is given in some literatures . The authors have presented a new definition of fractional derivative and fractional integral, and in Abdeljawad, the basic concepts in a new simple interesting fractional calculus have been investigated.…”

Homotopy Analysis Method for Conformable Burgers-Korteweg-de Vries Equation

“…For example T. Abdeljawad [5] has presented conformable versions of the chain rule, exponential functions, Gronwalls inequality, integration by parts, Taylor power series expansions and Laplace transform. Iyiola et al [6] expressed the analytical solution of space-time fractional Fornberg-Whitham equation, Hesameddini et al [7] demonstrated the numerical solution of multi-order fractional differential equations via the sinc collocation method and K. R. Prasad et al [8] discussed prove the existence of multiple positive solutions for a coupled system of iterative type boundary value problems involving new conformable fractional order derivative. Therewithal to these studies O. Acan et al [9] introduced conformable fractional reduced differential transform method using Conformable Calculus and reduced differential transform method.…”