This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized integro-differential boundary conditions by utilizing contraction principle Banach Leray–Schauder fixed point theorems. Moreover, two different approaches, Hyers–Ulam stabilities are also discussed. Different ordinary third order (e.g., initial, an...

In this article, we deal with the existence of mild solutions for a class of fractional integro-differential equations with state-dependent delay. Our results are based on the technique of measures of noncompactness and Darbo’s fixed point theorem. An example is provided to illustrate the main result. AMS Subject Classifications: 26A33, 34A08, 34A37, 34G20, 34G25, 34H05, 34K09, 34K30.

Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed to solving such equations. We introduce the OHAM (Optimal Homotopy Asymptotic Method) for solving nonlinear integro-differential equations. Several examples for solving integro-differential equations are presented to illustrate the reliability ...

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results. Nowadays, fractional calculus receives increasing at...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

NEW ALGORITHMS FOR NUMERICAL SOLUTION OF NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF THIRD ORDER USING HAAR WAVELETS M. Fayyaz a and M. Azram b * Department of Computer Science, CECOS University Peshawar, Pakistan. [email protected] b Faculty of Engineering, IIUM, Kuala Lumpur 50728, Malaysia. [email protected] ABSTRACT: This paper deals with the extension of earlier work [3] (designed for Fre...

the main purpose of this paper is to consider adomian's decomposition method in non-linear volterra integro-differential equations. the advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of adomian's method applied to such nonlinear integro-differential equations are discussed. finall...

Using a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of S-asymptotically !-periodic mild solutions for a class of linear and semilinear fractional order differential equations of the form D +1 t u(t) + D t u(t)−Au(t) = f(t, u(t)), t > 0, 0 < ≤ ≤ 1, ≥ 0.