This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...

in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

Motivated by the requirement for pinpoint landing in futureMarsmissions, we consider the problemofminimumfuel powered terminal descent to a prescribed landing site. The first-order necessary conditions are derived and interpreted for a point-mass model with throttle and thrust angle control and for rigid-bodymodel with throttle and angular velocity control, clarifying the characteristics of the...

Exact solutions of higher-dimensional nonlinear equations takes a major place in the study phenomena observed nature. In this article, some new kink type are investigated for (3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP) equation. Firstly, variety obtained by Hirota’s bilinear form, which include wave solution, periodic solitary and singular using extended homoclinic test approach. Second...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

A new concept of “an imperfect singular solution” is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration. key wor...

By using quasi–derivatives, we develop a Fourier method for studying the spectral properties of one dimensional Schrödinger operators with periodic singular potentials.

Some classical tools have been used in the literature to study the positive solutions for twopoint boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see 1–3 and literatures therein. Recently, Schauder’s fixed point theore...