In this paper, we use integral equations of non-integer orders to derive discrete maps with memory. Note that memory were not previously derived from fractional orders. Such a derivation is proposed for the first time in work. nonlocality and exact solutions Riemann–Liouville Hadamard type integrals periodic sequence kicks are described by Dirac delta-functions. The suggested these without any ...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

In this article, we study basic properties of exp-convex functions and establish the corresponding Hadamard type integral inequalities along with fractional operators. A comparative analysis between exp-convexity classic convexity is discussed. Furthermore, several related identities estimation upper bounds involved operators are proved. addition, some indispensable propositions associated spec...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

By Hölder's integral inequality, the authors establish some Hermite-Hadamard type integral inequalities for n-times differentiable and geometrically quasi-convex functions.

The paper presents a new fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases. Conditions are given for such a generalized fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for th...

In the present research, we initiate study of boundary value problems for sequential Riemann–Liouville and Hadamard–Caputo fractional derivatives, supplemented with iterated integral conditions. Firstly, convert given nonlinear problem into a fixed point by considering linear variant problem. Once operator is available, use variety theorems to establish results regarding existence uniqueness. S...