In this paper, we present an approximate method for solving integro-differential equations of multi-fractional order by using the variational iteration method.
First, we derive the variational iteration formula related to the considered problem, then prove its convergence to the exact solution. Also we give some illustrative examples of linear and nonlinear equations.

Introduction: Cutaneous leishmaniasis (CL) is a common protozoan disease in Iraq characterized by localized ulcers, primarily on exposed skin. This study aimed to investigate the hematological parameters of infected patients using a complete blood count (CBC) in the endemic area of Diyala Governorate, northeast of Baghdad. This has been studied in newly diagnosed, untreated individuals and patients receiving sodium antimony gluconate. Methodology: Hematological screening was performed on blood samples from 161 patients with microscopically diagnosed cutaneous leishmaniasis before and after treatment. Anti-Leishmania IgG was also assessed by ELISA in seropositive and seronegative subjects. Results: The newly diagnosed, untreated pati

Complex-valued regular functions that are normalized in the open unit disk are vastly studied. The current study introduces a new fractional integrodifferential (non-linear) operator. Based on the pre-Schwarzian derivative, certain appropriate stipulations on the parameters included in this con-structed operator to be univalent and bounded are investigated and determined.

      In this paper, several types of space-time fractional partial differential equations has been solved by using most of special double linear integral transform ”double  Sumudu ”. Also, we are going to argue the truth of these solutions by another analytically method “invariant subspace method”. All results are illustrative numerically and graphically.

Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems

       In this work, the fractional damped Burger's equation (FDBE) formula    = 0,

     This is a contribution to study the complex effect of rainfall on the incidence of cutaneous leishmaniasis in an endemic area (AL-Mohalabiya) in Ninava province in the north region of Iraq.
 

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

The main goal of this paper is to study applications of the fractional calculus techniques for a certain subclass of multivalent analytic functions on Hilbert Space. Also, we obtain the coefficient estimates, extreme points, convex combination and hadamard product.

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions.